diff --git a/lib/matplotlib/_c_internal_utils.pyi b/lib/matplotlib/_c_internal_utils.pyi
index 3efc81bc8332..ccc172cde27a 100644
--- a/lib/matplotlib/_c_internal_utils.pyi
+++ b/lib/matplotlib/_c_internal_utils.pyi
@@ -1,4 +1,5 @@
 def display_is_valid() -> bool: ...
+def xdisplay_is_valid() -> bool: ...
 
 def Win32_GetForegroundWindow() -> int | None: ...
 def Win32_SetForegroundWindow(hwnd: int) -> None: ...
diff --git a/lib/matplotlib/cbook.py b/lib/matplotlib/cbook.py
index cff8f02fd349..7cf32c4d5f6a 100644
--- a/lib/matplotlib/cbook.py
+++ b/lib/matplotlib/cbook.py
@@ -72,7 +72,7 @@ def _get_running_interactive_framework():
                 if frame.f_code in codes:
                     return "tk"
                 frame = frame.f_back
-        # premetively break reference cycle between locals and the frame
+        # Preemptively break reference cycle between locals and the frame.
         del frame
     macosx = sys.modules.get("matplotlib.backends._macosx")
     if macosx and macosx.event_loop_is_running():
diff --git a/lib/matplotlib/tests/test_backend_tk.py b/lib/matplotlib/tests/test_backend_tk.py
index ee20a94042f7..89782e8a66f3 100644
--- a/lib/matplotlib/tests/test_backend_tk.py
+++ b/lib/matplotlib/tests/test_backend_tk.py
@@ -35,8 +35,8 @@ def _isolated_tk_test(success_count, func=None):
         reason="missing tkinter"
     )
     @pytest.mark.skipif(
-        sys.platform == "linux" and not _c_internal_utils.display_is_valid(),
-        reason="$DISPLAY and $WAYLAND_DISPLAY are unset"
+        sys.platform == "linux" and not _c_internal_utils.xdisplay_is_valid(),
+        reason="$DISPLAY is unset"
     )
     @pytest.mark.xfail(  # https://github.com/actions/setup-python/issues/649
         ('TF_BUILD' in os.environ or 'GITHUB_ACTION' in os.environ) and
diff --git a/lib/matplotlib/tests/test_backends_interactive.py b/lib/matplotlib/tests/test_backends_interactive.py
index 2c6b61a48438..ca702bc1d99c 100644
--- a/lib/matplotlib/tests/test_backends_interactive.py
+++ b/lib/matplotlib/tests/test_backends_interactive.py
@@ -57,6 +57,8 @@ def wait_for(self, terminator):
 def _get_available_interactive_backends():
     _is_linux_and_display_invalid = (sys.platform == "linux" and
                                      not _c_internal_utils.display_is_valid())
+    _is_linux_and_xdisplay_invalid = (sys.platform == "linux" and
+                                      not _c_internal_utils.xdisplay_is_valid())
     envs = []
     for deps, env in [
             *[([qt_api],
@@ -74,10 +76,12 @@ def _get_available_interactive_backends():
     ]:
         reason = None
         missing = [dep for dep in deps if not importlib.util.find_spec(dep)]
-        if _is_linux_and_display_invalid:
-            reason = "$DISPLAY and $WAYLAND_DISPLAY are unset"
-        elif missing:
+        if missing:
             reason = "{} cannot be imported".format(", ".join(missing))
+        elif env["MPLBACKEND"] == "tkagg" and _is_linux_and_xdisplay_invalid:
+            reason = "$DISPLAY is unset"
+        elif _is_linux_and_display_invalid:
+            reason = "$DISPLAY and $WAYLAND_DISPLAY are unset"
         elif env["MPLBACKEND"] == 'macosx' and os.environ.get('TF_BUILD'):
             reason = "macosx backend fails on Azure"
         elif env["MPLBACKEND"].startswith('gtk'):
diff --git a/lib/matplotlib/tests/test_rcparams.py b/lib/matplotlib/tests/test_rcparams.py
index 4823df0ce250..25ae258ffcbb 100644
--- a/lib/matplotlib/tests/test_rcparams.py
+++ b/lib/matplotlib/tests/test_rcparams.py
@@ -536,7 +536,7 @@ def test_backend_fallback_headless(tmp_path):
 
 
 @pytest.mark.skipif(
-    sys.platform == "linux" and not _c_internal_utils.display_is_valid(),
+    sys.platform == "linux" and not _c_internal_utils.xdisplay_is_valid(),
     reason="headless")
 def test_backend_fallback_headful(tmp_path):
     pytest.importorskip("tkinter")
diff --git a/src/_c_internal_utils.cpp b/src/_c_internal_utils.cpp
index 74bb97904f89..561cb303639c 100644
--- a/src/_c_internal_utils.cpp
+++ b/src/_c_internal_utils.cpp
@@ -33,7 +33,7 @@ namespace py = pybind11;
 using namespace pybind11::literals;
 
 static bool
-mpl_display_is_valid(void)
+mpl_xdisplay_is_valid(void)
 {
 #ifdef __linux__
     void* libX11;
@@ -57,6 +57,19 @@ mpl_display_is_valid(void)
             return true;
         }
     }
+    return false;
+#else
+    return true;
+#endif
+}
+
+static bool
+mpl_display_is_valid(void)
+{
+#ifdef __linux__
+    if (mpl_xdisplay_is_valid()) {
+        return true;
+    }
     void* libwayland_client;
     if (getenv("WAYLAND_DISPLAY")
         && (libwayland_client = dlopen("libwayland-client.so.0", RTLD_LAZY))) {
@@ -194,6 +207,16 @@ PYBIND11_MODULE(_c_internal_utils, m)
         succeeds, or $WAYLAND_DISPLAY is set and wl_display_connect(NULL)
         succeeds.
 
+        On other platforms, always returns True.)""");
+    m.def(
+        "xdisplay_is_valid", &mpl_xdisplay_is_valid,
+        R"""(        --
+        Check whether the current X11 display is valid.
+
+        On Linux, returns True if either $DISPLAY is set and XOpenDisplay(NULL)
+        succeeds. Use this function if you need to specifically check for X11
+        only (e.g., for Tkinter).
+
         On other platforms, always returns True.)""");
     m.def(
         "Win32_GetCurrentProcessExplicitAppUserModelID",