diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 712971192a4..4df2ffd1db7 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -168,6 +168,11 @@ Bug Fixes
   the array. Previously, e.g. ``da.cumulative("time").argmax()`` returned indices
   shifted by the number of missing values in front of the array (:issue:`11336`).
   By `Michael Niklas <https://github.com/headtr1ck>`_.
+- :py:meth:`DataArray.str.replace` now respects ``case=False`` when ``regex=False``;
+  the option was silently ignored. :py:meth:`DataArray.str.contains` with
+  ``case=False, regex=False`` no longer raises ``AttributeError`` on object-dtype
+  or ``StringDType`` arrays (:pull:`11747`).
+  By `Novain Shibu <https://github.com/novain-shibu>`_.
 - Fix :py:func:`tutorial.open_dataset` and :py:func:`tutorial.open_datatree`
   with ``cache=False`` failing on Windows, because the downloaded file was
   removed while still open (:pull:`11703`).
diff --git a/xarray/core/accessor_str.py b/xarray/core/accessor_str.py
index 103de9e20c1..fb13f53d70d 100644
--- a/xarray/core/accessor_str.py
+++ b/xarray/core/accessor_str.py
@@ -1520,14 +1520,10 @@ def func(x, ipat):
             pat = self._stringify(pat)
             if case or case is None:
                 func = lambda x, ipat: ipat in x
-            elif self._obj.dtype.char == "U":
-                uppered = self.casefold()
-                uppat = StringAccessor(pat).casefold()  # type: ignore[type-var]  # hack?
-                return uppered.str.contains(uppat, regex=False)  # type: ignore[return-value]
+            elif self._obj.dtype.kind == "S":
+                func = lambda x, ipat: ipat.upper() in x.upper()
             else:
-                uppered = self.upper()
-                uppat = StringAccessor(pat).upper()  # type: ignore[type-var]  # hack?
-                return uppered.str.contains(uppat, regex=False)  # type: ignore[return-value]
+                func = lambda x, ipat: ipat.casefold() in x.casefold()
 
         return self._apply(func=func, func_args=(pat,), dtype=bool)
 
@@ -1962,7 +1958,22 @@ def replace(
             )
         else:
             pat = self._stringify(pat)
-            func = lambda x, ipat, irepl, i_n: x.replace(ipat, irepl, i_n)
+            if case is False:
+                # Literal match, but case-insensitive: escape the pattern and
+                # return the replacement as-is so it is not parsed as a template.
+                func = lambda x, ipat, irepl, i_n: (
+                    x
+                    if i_n == 0
+                    else re.sub(
+                        re.escape(ipat),
+                        lambda _: irepl,
+                        x,
+                        count=max(i_n, 0),
+                        flags=re.IGNORECASE,
+                    )
+                )
+            else:
+                func = lambda x, ipat, irepl, i_n: x.replace(ipat, irepl, i_n)
         return self._apply(func=func, func_args=(pat, repl, n))
 
     def extract(
diff --git a/xarray/tests/test_accessor_str.py b/xarray/tests/test_accessor_str.py
index 55ba2b55f5e..e71558aaca1 100644
--- a/xarray/tests/test_accessor_str.py
+++ b/xarray/tests/test_accessor_str.py
@@ -403,6 +403,52 @@ def test_replace_n_zero(dtype) -> None:
     assert_equal(result, expected)
 
 
+def test_replace_literal_case_insensitive(dtype) -> None:
+    values = xr.DataArray(["fooBAD.bad__barbAd"], dims=["x"]).astype(dtype)
+
+    result = values.str.replace("bad", "X", case=False, regex=False)
+    expected = xr.DataArray(["fooX.X__barX"], dims=["x"]).astype(dtype)
+    assert result.dtype == expected.dtype
+    assert_equal(result, expected)
+
+    # the pattern is literal, and the replacement is not a regex template
+    result = values.str.replace("D.B", r"
", n=1, case=False, regex=False)
+    expected = xr.DataArray([r"fooBA
ad__barbAd"], dims=["x"]).astype(dtype)
+    assert result.dtype == expected.dtype
+    assert_equal(result, expected)
+
+    result = values.str.replace("bad", "X", n=2, case=False, regex=False)
+    expected = xr.DataArray(["fooX.X__barbAd"], dims=["x"]).astype(dtype)
+    assert_equal(result, expected)
+
+    result = values.str.replace("bad", "X", n=0, case=False, regex=False)
+    assert_equal(result, values)
+
+
+@pytest.mark.parametrize(
+    "values",
+    [
+        pytest.param(np.array(["Foo", "xYz", "fOO.oo"], dtype=object), id="object"),
+        pytest.param(
+            np.array(["Foo", "xYz", "fOO.oo"], dtype=np.dtypes.StringDType()),
+            id="StringDType",
+        ),
+    ],
+)
+def test_case_insensitive_literal_non_unicode_dtype(values) -> None:
+    da = xr.DataArray(values, dims=["x"])
+
+    result = da.str.contains("o.", case=False, regex=False)
+    assert_equal(result, xr.DataArray([False, False, True], dims=["x"]))
+
+    result = da.str.replace("o", "_", case=False, regex=False)
+    expected = xr.DataArray(
+        np.array(["F__", "xYz", "f__.__"], dtype=values.dtype), dims=["x"]
+    )
+    assert result.dtype == expected.dtype
+    assert_equal(result, expected)
+
+
 def test_replace_callable() -> None:
     values = xr.DataArray(["fooBAD__barBAD"])