diff --git a/Lib/statistics.py b/Lib/statistics.py
index ad4a94219cf38c..c71e83aa7887d3 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -1206,9 +1206,14 @@ def stdev(data, xbar=None):
     if n < 2:
         raise StatisticsError('stdev requires at least two data points')
     mss = ss / (n - 1)
+    try:
+        mss_numerator = mss.numerator
+        mss_denominator = mss.denominator
+    except AttributeError:
+        raise ValueError('inf or nan encountered in data')
     if issubclass(T, Decimal):
-        return _decimal_sqrt_of_frac(mss.numerator, mss.denominator)
-    return _float_sqrt_of_frac(mss.numerator, mss.denominator)
+        return _decimal_sqrt_of_frac(mss_numerator, mss_denominator)
+    return _float_sqrt_of_frac(mss_numerator, mss_denominator)
 
 
 def pstdev(data, mu=None):
@@ -1224,9 +1229,14 @@ def pstdev(data, mu=None):
     if n < 1:
         raise StatisticsError('pstdev requires at least one data point')
     mss = ss / n
+    try:
+        mss_numerator = mss.numerator
+        mss_denominator = mss.denominator
+    except AttributeError:
+        raise ValueError('inf or nan encountered in data')
     if issubclass(T, Decimal):
-        return _decimal_sqrt_of_frac(mss.numerator, mss.denominator)
-    return _float_sqrt_of_frac(mss.numerator, mss.denominator)
+        return _decimal_sqrt_of_frac(mss_numerator, mss_denominator)
+    return _float_sqrt_of_frac(mss_numerator, mss_denominator)
 
 
 def _mean_stdev(data):
diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
index 40599c776a6a80..f51512bf419270 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -2122,6 +2122,14 @@ def test_center_not_at_mean(self):
         self.assertEqual(self.func(data), 2.5)
         self.assertEqual(self.func(data, mu=0.5), 6.5)
 
+    def test_gh_140938(self):
+        # Inputs with inf/nan should raise a ValueError
+        with self.assertRaises(ValueError):
+            self.func([1.0, math.inf])
+        with self.assertRaises(ValueError):
+            self.func([1.0, math.nan])
+
+
 class TestSqrtHelpers(unittest.TestCase):
 
     def test_integer_sqrt_of_frac_rto(self):
@@ -2240,6 +2248,14 @@ def test_center_not_at_mean(self):
         data = (1.0, 2.0)
         self.assertEqual(self.func(data, xbar=2.0), 1.0)
 
+    def test_gh_140938(self):
+        # Inputs with inf/nan should raise a ValueError
+        with self.assertRaises(ValueError):
+            self.func([1.0, math.inf])
+        with self.assertRaises(ValueError):
+            self.func([1.0, math.nan])
+
+
 class TestGeometricMean(unittest.TestCase):
 
     def test_basics(self):
diff --git a/Misc/NEWS.d/next/Library/2025-11-13-14-51-30.gh-issue-140938.kXsHHv.rst b/Misc/NEWS.d/next/Library/2025-11-13-14-51-30.gh-issue-140938.kXsHHv.rst
new file mode 100644
index 00000000000000..bd3044002a2d54
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2025-11-13-14-51-30.gh-issue-140938.kXsHHv.rst
@@ -0,0 +1,2 @@
+The :func:`statistics.stdev` and :func:`statistics.pstdev` functions now raise a
+:exc:`ValueError` when the input contains an infinity or a NaN.