diff --git a/Doc/library/io.rst b/Doc/library/io.rst
index 969b4080f7a..d50e66501b4 100644
--- a/Doc/library/io.rst
+++ b/Doc/library/io.rst
@@ -233,7 +233,7 @@ I/O Base Classes
    :class:`IOBase` object can be iterated over yielding the lines in a stream.
    Lines are defined slightly differently depending on whether the stream is
    a binary stream (yielding :class:`bytes`), or a text stream (yielding
-   :class:`unicode` strings).  See :meth:`readline` below.
+   :class:`unicode` strings).  See :meth:`~IOBase.readline` below.
 
    IOBase is also a context manager and therefore supports the
    :keyword:`with` statement.  In this example, *file* is closed after the
diff --git a/Misc/NEWS b/Misc/NEWS
index ef069603238..4c45a854ff3 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -430,6 +430,9 @@ Tests
 Documentation
 -------------
 
+- Issue #13513: Fix io.IOBase documentation to correctly link to the
+  io.IOBase.readline method instead of the readline module.
+
 - Issue #13237: Reorganise subprocess documentation to emphasise convenience
   functions and the most commonly needed arguments to Popen.