diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2026-10-21-21-26-10.gh-issue-159739.Zw43uX.rst b/Misc/NEWS.d/next/Core_and_Builtins/2026-10-21-21-26-10.gh-issue-159739.Zw43uX.rst
new file mode 100644
index 000000000000000..628a146b059a436
--- /dev/null
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2026-10-21-21-26-10.gh-issue-159739.Zw43uX.rst
@@ -0,0 +1 @@
+Raise :exc:`MemoryError` instead of returning an incorrect result if :func:`round` runs out of memory while rounding a float.
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index d5a879cdd53ad62..c19ed6e6b609352 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -942,11 +942,16 @@ double_round(double x, int ndigits) {
     _Py_SET_53BIT_PRECISION_START;
     rounded = _Py_dg_strtod(mybuf, NULL);
     _Py_SET_53BIT_PRECISION_END;
-    if (errno == ERANGE && fabs(rounded) >= 1.)
+    if (errno == ENOMEM) {
+        PyErr_NoMemory();
+    }
+    else if (errno == ERANGE && fabs(rounded) >= 1.) {
         PyErr_SetString(PyExc_OverflowError,
                         "rounded value too large to represent");
-    else
+    }
+    else {
         result = PyFloat_FromDouble(rounded);
+    }
 
     /* done computing value;  now clean up */
     if (mybuf != shortbuf)