diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index c6c4dadaf8c9d..b686bcf690e8f 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -782,6 +782,7 @@ Strings
 - Bug in the conversion from ``pyarrow.ChunkedArray`` to :class:`~arrays.StringArray` when the original had zero chunks (:issue:`41040`)
 - Bug in :meth:`Series.replace` and :meth:`DataFrame.replace` ignoring replacements with ``regex=True`` for ``StringDType`` data (:issue:`41333`, :issue:`35977`)
 - Bug in :meth:`Series.str.extract` with :class:`~arrays.StringArray` returning object dtype for empty :class:`DataFrame` (:issue:`41441`)
+- Bug in :meth:`Series.str.replace` where the ``case`` argument was ignored when ``regex=False`` (:issue:`41602`)
 
 Interval
 ^^^^^^^^
diff --git a/pandas/core/strings/accessor.py b/pandas/core/strings/accessor.py
index 8e6f4bfd3b320..ca0067b77ee23 100644
--- a/pandas/core/strings/accessor.py
+++ b/pandas/core/strings/accessor.py
@@ -1358,14 +1358,13 @@ def replace(
                         "*not* be treated as literal strings when regex=True."
                     )
                 warnings.warn(msg, FutureWarning, stacklevel=3)
-            regex = True
 
         # Check whether repl is valid (GH 13438, GH 15055)
         if not (isinstance(repl, str) or callable(repl)):
             raise TypeError("repl must be a string or callable")
 
         is_compiled_re = is_re(pat)
-        if regex:
+        if regex or regex is None:
             if is_compiled_re and (case is not None or flags != 0):
                 raise ValueError(
                     "case and flags cannot be set when pat is a compiled regex"
@@ -1378,6 +1377,14 @@ def replace(
         elif callable(repl):
             raise ValueError("Cannot use a callable replacement when regex=False")
 
+        # The current behavior is to treat single character patterns as literal strings,
+        # even when ``regex`` is set to ``True``.
+        if isinstance(pat, str) and len(pat) == 1:
+            regex = False
+
+        if regex is None:
+            regex = True
+
         if case is None:
             case = True
 
diff --git a/pandas/core/strings/object_array.py b/pandas/core/strings/object_array.py
index fb9fd77d21732..c214ada9c1ada 100644
--- a/pandas/core/strings/object_array.py
+++ b/pandas/core/strings/object_array.py
@@ -145,10 +145,10 @@ def _str_replace(
             # add case flag, if provided
             flags |= re.IGNORECASE
 
-        if regex and (
-            isinstance(pat, re.Pattern) or len(pat) > 1 or flags or callable(repl)
-        ):
+        if regex or flags or callable(repl):
             if not isinstance(pat, re.Pattern):
+                if regex is False:
+                    pat = re.escape(pat)
                 pat = re.compile(pat, flags=flags)
 
             n = n if n >= 0 else 0
diff --git a/pandas/tests/strings/test_find_replace.py b/pandas/tests/strings/test_find_replace.py
index 2104b50c5121a..391c71e57399a 100644
--- a/pandas/tests/strings/test_find_replace.py
+++ b/pandas/tests/strings/test_find_replace.py
@@ -555,6 +555,19 @@ def test_replace_moar(any_string_dtype):
     tm.assert_series_equal(result, expected)
 
 
+def test_replace_not_case_sensitive_not_regex(any_string_dtype):
+    # https://github.com/pandas-dev/pandas/issues/41602
+    ser = Series(["A.", "a.", "Ab", "ab", np.nan], dtype=any_string_dtype)
+
+    result = ser.str.replace("a", "c", case=False, regex=False)
+    expected = Series(["c.", "c.", "cb", "cb", np.nan], dtype=any_string_dtype)
+    tm.assert_series_equal(result, expected)
+
+    result = ser.str.replace("a.", "c.", case=False, regex=False)
+    expected = Series(["c.", "c.", "Ab", "ab", np.nan], dtype=any_string_dtype)
+    tm.assert_series_equal(result, expected)
+
+
 def test_replace_regex_default_warning(any_string_dtype):
     # https://github.com/pandas-dev/pandas/pull/24809
     s = Series(["a", "b", "ac", np.nan, ""], dtype=any_string_dtype)