diff --git a/changelog/4739.bugfix.rst b/changelog/4739.bugfix.rst
new file mode 100644
index 000000000..dcd44d3fa
--- /dev/null
+++ b/changelog/4739.bugfix.rst
@@ -0,0 +1 @@
+Fix ``parametrize(... ids=<function>)`` when the function returns non-strings.
diff --git a/src/_pytest/python.py b/src/_pytest/python.py
index 85373f47c..aaa49f7dd 100644
--- a/src/_pytest/python.py
+++ b/src/_pytest/python.py
@@ -1144,9 +1144,10 @@ def _find_parametrized_scope(argnames, arg2fixturedefs, indirect):
 
 def _idval(val, argname, idx, idfn, item, config):
     if idfn:
-        s = None
         try:
-            s = idfn(val)
+            generated_id = idfn(val)
+            if generated_id is not None:
+                val = generated_id
         except Exception as e:
             # See issue https://github.com/pytest-dev/pytest/issues/2169
             msg = "{}: error raised while trying to determine id of parameter '{}' at position {}\n"
@@ -1154,10 +1155,7 @@ def _idval(val, argname, idx, idfn, item, config):
             # we only append the exception type and message because on Python 2 reraise does nothing
             msg += "  {}: {}\n".format(type(e).__name__, e)
             six.raise_from(ValueError(msg), e)
-        if s:
-            return ascii_escaped(s)
-
-    if config:
+    elif config:
         hook_id = config.hook.pytest_make_parametrize_id(
             config=config, val=val, argname=argname
         )
diff --git a/testing/python/metafunc.py b/testing/python/metafunc.py
index 5c352efd1..fa22966d8 100644
--- a/testing/python/metafunc.py
+++ b/testing/python/metafunc.py
@@ -418,6 +418,21 @@ class TestMetafunc(object):
             ]
         )
 
+    def test_parametrize_ids_returns_non_string(self, testdir):
+        testdir.makepyfile(
+            """\
+            import pytest
+
+            def ids(d):
+                return d
+
+            @pytest.mark.parametrize("arg", ({1: 2}, {3, 4}), ids=ids)
+            def test(arg):
+                assert arg
+            """
+        )
+        assert testdir.runpytest().ret == 0
+
     def test_idmaker_with_ids(self):
         from _pytest.python import idmaker