diff --git a/CHANGES.rst b/CHANGES.rst
index 232b144a5c..71d327bbfc 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -28,6 +28,9 @@ Unreleased
     it's disabled in config. Previously, only disabling worked. :issue:`5916`
 -   ``Flask.select_jinja_autoescape`` uses case-insensitive comparison instead
     of only lower case file extensions. :pr:`6012`
+-   Add ``allow_nan`` attribute to ``DefaultJSONProvider`` to control whether
+    ``NaN`` and ``Infinity`` values are allowed when serializing to JSON.
+    Defaults to ``True`` to preserve existing behavior. :issue:`6114`
 
 
 Version 3.1.3
diff --git a/src/flask/json/provider.py b/src/flask/json/provider.py
index f37cb7b209..71756d8951 100644
--- a/src/flask/json/provider.py
+++ b/src/flask/json/provider.py
@@ -160,6 +160,15 @@ class DefaultJSONProvider(JSONProvider):
     or ``None`` in debug mode, it will use a non-compact representation.
     """
 
+    allow_nan = True
+    """Allow ``NaN``, ``Infinity``, and ``-Infinity`` to be serialized as
+    the bare literals ``NaN``, ``Infinity``, and ``-Infinity``. These are
+    accepted by Python's :mod:`json` but are not valid JSON per
+    :rfc:`8259`, so strict parsers such as a browser's ``JSON.parse``
+    will reject them. Set this to ``False`` to raise a ``ValueError``
+    instead when such a value is serialized.
+    """
+
     mimetype = "application/json"
     """The mimetype set in :meth:`response`."""
 
@@ -168,7 +177,8 @@ def dumps(self, obj: t.Any, **kwargs: t.Any) -> str:
 
         Keyword arguments are passed to :func:`json.dumps`. Sets some
         parameter defaults from the :attr:`default`,
-        :attr:`ensure_ascii`, and :attr:`sort_keys` attributes.
+        :attr:`ensure_ascii`, :attr:`sort_keys`, and :attr:`allow_nan`
+        attributes.
 
         :param obj: The data to serialize.
         :param kwargs: Passed to :func:`json.dumps`.
@@ -176,6 +186,7 @@ def dumps(self, obj: t.Any, **kwargs: t.Any) -> str:
         kwargs.setdefault("default", self.default)
         kwargs.setdefault("ensure_ascii", self.ensure_ascii)
         kwargs.setdefault("sort_keys", self.sort_keys)
+        kwargs.setdefault("allow_nan", self.allow_nan)
         return json.dumps(obj, **kwargs)
 
     def loads(self, s: str | bytes, **kwargs: t.Any) -> t.Any:
diff --git a/tests/test_json.py b/tests/test_json.py
index 1e2b27dc9c..11af91f9ec 100644
--- a/tests/test_json.py
+++ b/tests/test_json.py
@@ -54,6 +54,16 @@ def test_json_as_unicode(test_value, expected, app, app_ctx):
     assert rv == expected
 
 
+def test_json_allow_nan(app, app_ctx):
+    assert app.json.allow_nan
+    rv = app.json.dumps(float("nan"))
+    assert rv == "NaN"
+
+    app.json.allow_nan = False
+    with pytest.raises(ValueError):
+        app.json.dumps(float("nan"))
+
+
 def test_json_dump_to_file(app, app_ctx):
     test_data = {"name": "Flask"}
     out = io.StringIO()