diff --git a/CHANGES b/CHANGES
index 66bc5f17..61794d12 100644
--- a/CHANGES
+++ b/CHANGES
@@ -10,6 +10,12 @@
 * Fixed `fragment_identifier_matcher` treating opaque fragments (those without
   ``=``, e.g. ``/users/5``) as always equal, so a required fragment matched a
   different one or none at all. See #806
+* Fixed `responses` mutating the live `PreparedRequest` object that `requests`
+  threads back to the caller (e.g. attached to a raised exception's
+  ``.request``, or the outer ``Response.request``) with internal-use
+  ``params``/``req_kwargs`` attributes. These attributes are now only
+  attached to the request object exposed via ``responses.calls[i].request``.
+  See #738
 
 0.26.2
 ------
diff --git a/README.rst b/README.rst
index a5a8bb0e..2dd3ce41 100644
--- a/README.rst
+++ b/README.rst
@@ -368,7 +368,10 @@ deprecated argument.
         constructed_url = r"http://example.com/test?I+am=a+big+test&hello=world"
         assert resp.url == constructed_url
         assert resp.request.url == constructed_url
-        assert resp.request.params == params
+        # ``params`` is only available on ``responses.calls[i].request``, not on the
+        # actual request/response objects returned to the caller, so that mocked
+        # requests don't expose responses-internal attributes to production code.
+        assert responses.calls[0].request.params == params
 
 By default, matcher will validate that all parameters match strictly.
 To validate that only parameters specified in the matcher are present in original request
diff --git a/responses/__init__.py b/responses/__init__.py
index 41f5fde8..dca64eeb 100644
--- a/responses/__init__.py
+++ b/responses/__init__.py
@@ -1,3 +1,4 @@
+import copy
 import inspect
 import json as json_module
 import logging
@@ -1104,6 +1105,16 @@ def _on_request(
         match, match_failed_reasons = self._find_match(request)
         resp_callback = self.response_callback
 
+        # `request` is the same live PreparedRequest object that `requests` threads
+        # back to the caller (e.g. via a raised exception's `.request`, or the
+        # outer `Response.request`), so it must not carry responses-internal
+        # attributes. Keep a copy with those attributes attached for use only in
+        # the internal call log (`responses.calls`), and strip them off the
+        # object that flows back to the caller. See GH #738.
+        call_request = copy.copy(request)
+        del request.params  # type: ignore[attr-defined]
+        del request.req_kwargs  # type: ignore[attr-defined]
+
         if match is None:
             if any(
                 [
@@ -1136,7 +1147,7 @@ def _on_request(
             response = ConnectionError(error_msg)
             response.request = request
 
-            self._calls.add(request, response)
+            self._calls.add(call_request, response)
             raise response
 
         if match.passthrough:
@@ -1148,14 +1159,14 @@ def _on_request(
                     request, match.get_response(request)
                 )
             except BaseException as response:
-                call = Call(request, response)
+                call = Call(call_request, response)
                 self._calls.add_call(call)
                 match.calls.add_call(call)
                 raise
 
         if resp_callback:
             response = resp_callback(response)  # type: ignore[misc]
-        call = Call(request, response)  # type: ignore[misc]
+        call = Call(call_request, response)  # type: ignore[misc]
         self._calls.add_call(call)
         match.calls.add_call(call)
 
diff --git a/responses/tests/test_matchers.py b/responses/tests/test_matchers.py
index 8eefce69..f89cfeaa 100644
--- a/responses/tests/test_matchers.py
+++ b/responses/tests/test_matchers.py
@@ -583,8 +583,12 @@ def run():
         assert resp.url == constructed_url
         assert resp.request.url == constructed_url
 
-        resp_params = getattr(resp.request, "params")
-        assert resp_params == params
+        # `params` is a responses-internal attribute and is only exposed via
+        # `responses.calls[i].request`, not on the live request/response
+        # objects returned to the caller. See GH #738.
+        assert not hasattr(resp.request, "params")
+        call_params = getattr(responses.calls[0].request, "params")
+        assert call_params == params
 
     run()
     assert_reset()
diff --git a/responses/tests/test_responses.py b/responses/tests/test_responses.py
index b3740ed9..a6543b97 100644
--- a/responses/tests/test_responses.py
+++ b/responses/tests/test_responses.py
@@ -48,11 +48,19 @@ def assert_response(
 
 
 def assert_params(resp, expected):
+    # NOTE: `params`/`req_kwargs` are responses-internal attributes and are
+    # intentionally only exposed via `responses.calls[i].request`, not on the
+    # actual request/response objects returned to the caller. See GH #738.
     assert hasattr(resp, "request"), "Missing request"
-    assert hasattr(
+    assert not hasattr(
         resp.request, "params"
-    ), "Missing params on request that responses should add"
-    assert getattr(resp.request, "params") == expected, "Incorrect parameters"
+    ), "params leaked onto the live request object returned to the caller"
+    assert len(responses.calls) >= 1, "Missing calls"
+    call_request = responses.calls[-1].request
+    assert hasattr(
+        call_request, "params"
+    ), "Missing params on responses.calls[-1].request that responses should add"
+    assert getattr(call_request, "params") == expected, "Incorrect parameters"
 
 
 def test_response():
@@ -354,6 +362,60 @@ def run():
     assert_reset()
 
 
+def test_response_params_not_leaked_to_caller_request():
+    """The live ``PreparedRequest`` object that `requests` threads back to the
+    caller (e.g. via a raised exception's ``.request``) must not carry
+    responses-internal ``params``/``req_kwargs`` attributes -- those exist
+    only on ``responses.calls[i].request`` as documented. See GH #738.
+    """
+
+    @responses.activate
+    def run():
+        url = "http://example.com/test"
+        params = {"hello": "world"}
+        responses.get(url, status=403)
+
+        with pytest.raises(HTTPError) as exc_info:
+            resp = requests.get(url, params=params)
+            resp.raise_for_status()
+
+        caught_request = exc_info.value.request
+        assert not hasattr(caught_request, "params")
+        assert not hasattr(caught_request, "req_kwargs")
+
+        # meanwhile, the documented convenience attributes are still available
+        # on the internal call log.
+        assert len(responses.calls) == 1
+        assert responses.calls[0].request.params == params
+        assert isinstance(responses.calls[0].request.req_kwargs, dict)
+
+    run()
+    assert_reset()
+
+
+def test_connection_error_request_params_not_leaked():
+    """Same guarantee as above, but for the ``ConnectionError`` raised when a
+    request doesn't match any registered mock.
+    """
+
+    @responses.activate
+    def run():
+        responses.add(responses.GET, "http://example.com")
+
+        with pytest.raises(ConnectionError) as exc_info:
+            requests.get("http://example.com/foo", params={"hello": "world"})
+
+        caught_request = exc_info.value.request
+        assert not hasattr(caught_request, "params")
+        assert not hasattr(caught_request, "req_kwargs")
+
+        assert len(responses.calls) == 1
+        assert responses.calls[0].request.params == {"hello": "world"}
+
+    run()
+    assert_reset()
+
+
 def test_match_querystring():
     @responses.activate
     def run():