diff --git a/CHANGELOG.md b/CHANGELOG.md
index 19d97b9..aad10a6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,7 @@
 **Fixes**:
 
 * [#539](https://github.com/alecthomas/voluptuous/pull/539): Raise `Invalid` instead of leaking `TypeError`/`ValueError` for non-numeric input to the `Number` validator
+* [#542](https://github.com/alecthomas/voluptuous/pull/542): Raise `Invalid` instead of leaking a raw `TypeError` for `Infinity`/`NaN` input to the `Number` validator
 
 ## [0.16.0]
 
diff --git a/voluptuous/tests/tests.py b/voluptuous/tests/tests.py
index 32a5b7a..0608548 100644
--- a/voluptuous/tests/tests.py
+++ b/voluptuous/tests/tests.py
@@ -1145,6 +1145,21 @@ def test_number_validation_with_non_numeric():
             assert False, "Did not raise Invalid for %r" % (value,)
 
 
+def test_number_validation_with_infinity_and_nan():
+    """Non-finite input raises Invalid, not a raw TypeError."""
+    schema = Schema({"number": Number(precision=6, scale=2)})
+    for value in ('Infinity', '-Infinity', 'NaN'):
+        try:
+            schema({"number": value})
+        except MultipleInvalid as e:
+            assert (
+                str(e)
+                == "Value must be a number enclosed with string for dictionary value @ data['number']"
+            )
+        else:
+            assert False, "Did not raise Invalid for %s" % value
+
+
 def test_number_validation_with_invalid_precision_invalid_scale():
     """Test with Number with invalid precision and scale"""
     schema = Schema({"number": Number(precision=6, scale=2)})
diff --git a/voluptuous/validators.py b/voluptuous/validators.py
index ddf1639..a69bb8a 100644
--- a/voluptuous/validators.py
+++ b/voluptuous/validators.py
@@ -1186,9 +1186,8 @@ def _get_precision_scale(self, number) -> typing.Tuple[int, int, Decimal]:
         if isinstance(exp, int):
             return (len(decimal_num.as_tuple().digits), -exp, decimal_num)
         else:
-            # TODO: handle infinity and NaN
-            # raise Invalid(self.msg or 'Value has no precision')
-            raise TypeError("infinity and NaN have no precision")
+            # Infinity/NaN have no precision; report as Invalid, not a raw TypeError.
+            raise Invalid(self.msg or 'Value must be a number enclosed with string')
 
 
 class SomeOf(_WithSubValidators):