diff --git a/Lib/test/test_signal.py b/Lib/test/test_signal.py
--- a/Lib/test/test_signal.py
+++ b/Lib/test/test_signal.py
@@ -519,12 +519,11 @@ class PthreadSigmaskTests(unittest.TestC
 
         # Issue #11998: The _tkinter module loads the Tcl library which creates
         # a thread waiting events in select(). This thread receives signals
-        # blocked by all other threads. We cannot test blocked signals if the
-        # _tkinter module is loaded.
-        can_test_blocked_signals = ('_tkinter' not in sys.modules)
-        if not can_test_blocked_signals:
-            print("WARNING: _tkinter is loaded, cannot test signals "
-                  "blocked by pthread_sigmask() (issue #11998)")
+        # blocked by all other threads. Finalize the Tcl library to exit the
+        # Tcl thread.
+        if '_tkinter' in sys.modules:
+            import _tkinter
+            _tkinter._finalize()
 
         # Install our signal handler
         old_handler = signal.signal(signum, handler)
@@ -539,8 +538,7 @@ class PthreadSigmaskTests(unittest.TestC
         # Block and then raise SIGUSR1. The signal is blocked: the signal
         # handler is not called, and the signal is now pending
         signal.pthread_sigmask(signal.SIG_BLOCK, [signum])
-        if can_test_blocked_signals:
-            os.kill(pid, signum)
+        os.kill(pid, signum)
 
         # Check the new mask
         blocked = read_sigmask()
@@ -548,11 +546,8 @@ class PthreadSigmaskTests(unittest.TestC
         self.assertEqual(set(old_mask) ^ set(blocked), {signum})
 
         # Unblock SIGUSR1
-        if can_test_blocked_signals:
-            with self.assertRaises(ZeroDivisionError):
-                # unblock the pending signal calls immediatly the signal handler
-                signal.pthread_sigmask(signal.SIG_UNBLOCK, [signum])
-        else:
+        with self.assertRaises(ZeroDivisionError):
+            # unblock the pending signal calls immediatly the signal handler
             signal.pthread_sigmask(signal.SIG_UNBLOCK, [signum])
         with self.assertRaises(ZeroDivisionError):
             os.kill(pid, signum)
diff --git a/Modules/_tkinter.c b/Modules/_tkinter.c
--- a/Modules/_tkinter.c
+++ b/Modules/_tkinter.c
@@ -2941,6 +2941,18 @@ static char getbusywaitinterval_doc[] =
 Return the current busy-wait interval between successive\n\
 calls to Tcl_DoOneEvent in a threaded Python interpreter.";
 
+static PyObject *
+Tkinter_finalize(PyObject *self, PyObject *args)
+{
+    Tcl_Finalize();
+    Py_RETURN_NONE;
+}
+
+static char finalize_doc[] =
+"_finalize()\n\
+\n\
+Finalize the Tcl library.";
+
 static PyMethodDef moduleMethods[] =
 {
     {"_flatten",           Tkinter_Flatten, METH_VARARGS},
@@ -2949,6 +2961,8 @@ static PyMethodDef moduleMethods[] =
                            setbusywaitinterval_doc},
     {"getbusywaitinterval",(PyCFunction)Tkinter_getbusywaitinterval,
                            METH_NOARGS, getbusywaitinterval_doc},
+    {"_finalize",          (PyCFunction)Tkinter_finalize,
+                           METH_NOARGS, finalize_doc},
     {NULL,                 NULL}
 };