diff --git a/include/pybind11/pytypes.h b/include/pybind11/pytypes.h
index 7a731e22..a837fb9f 100644
--- a/include/pybind11/pytypes.h
+++ b/include/pybind11/pytypes.h
@@ -473,6 +473,12 @@ struct error_fetch_and_normalize {
                           + " failed to obtain the name "
                             "of the normalized active exception type.");
         }
+#if defined(PYPY_VERSION)
+        // This behavior runs the risk of masking errors in the error handling, but avoids a
+        // conflict with PyPy, which relies on the normalization here to change OSError to
+        // FileNotFoundError (https://github.com/pybind/pybind11/issues/4075).
+        m_lazy_error_string = exc_type_name_norm;
+#else
         if (exc_type_name_norm != m_lazy_error_string) {
             std::string msg = std::string(called)
                               + ": MISMATCH of original and normalized "
@@ -484,6 +490,7 @@ struct error_fetch_and_normalize {
             msg += ": " + format_value_and_trace();
             pybind11_fail(msg);
         }
+#endif
     }
 
     error_fetch_and_normalize(const error_fetch_and_normalize &) = delete;
diff --git a/tests/test_exceptions.cpp b/tests/test_exceptions.cpp
index 3ec999d1..3583f22a 100644
--- a/tests/test_exceptions.cpp
+++ b/tests/test_exceptions.cpp
@@ -334,4 +334,14 @@ TEST_SUBMODULE(exceptions, m) {
             e.restore();
         }
     });
+
+    // https://github.com/pybind/pybind11/issues/4075
+    m.def("test_pypy_oserror_normalization", []() {
+        try {
+            py::module_::import("io").attr("open")("this_filename_must_not_exist", "r");
+        } catch (const py::error_already_set &e) {
+            return py::str(e.what()); // str must be built before e goes out of scope.
+        }
+        return py::str("UNEXPECTED");
+    });
 }
diff --git a/tests/test_exceptions.py b/tests/test_exceptions.py
index a5984a14..5e3beeed 100644
--- a/tests/test_exceptions.py
+++ b/tests/test_exceptions.py
@@ -360,3 +360,9 @@ def test_error_already_set_double_restore():
         "Internal error: pybind11::detail::error_fetch_and_normalize::restore()"
         " called a second time. ORIGINAL ERROR: ValueError: Random error."
     )
+
+
+def test_pypy_oserror_normalization():
+    # https://github.com/pybind/pybind11/issues/4075
+    what = m.test_pypy_oserror_normalization()
+    assert "this_filename_must_not_exist" in what