diff --git a/manim/mobject/svg/svg_mobject.py b/manim/mobject/svg/svg_mobject.py
index c296130a27..26834f7e0e 100644
--- a/manim/mobject/svg/svg_mobject.py
+++ b/manim/mobject/svg/svg_mobject.py
@@ -158,6 +158,15 @@ def __init__(
         )
         self.move_into_position()
 
+        # Glyph submobjects are added after super().__init__ set self.z_index,
+        # so a z_index passed to the constructor never reached them. Propagate
+        # it so the whole SVG (e.g. Text/MathTex) shares one z_index. Guard with
+        # getattr since the OpenGL renderer does not track z_index as an attribute.
+        z_index = getattr(self, "z_index", None)
+        if z_index is not None:
+            for submob in self.get_family():
+                submob.z_index = z_index
+
     def init_svg_mobject(self, use_svg_cache: bool) -> None:
         """Checks whether the SVG has already been imported and
         generates it if not.
diff --git a/tests/module/mobject/text/test_text_mobject.py b/tests/module/mobject/text/test_text_mobject.py
index 2e656b90ae..a3f446e019 100644
--- a/tests/module/mobject/text/test_text_mobject.py
+++ b/tests/module/mobject/text/test_text_mobject.py
@@ -17,6 +17,21 @@ def test_font_size():
     assert round(markuptext_string.font_size, 5) == 14.4
 
 
+def test_z_index_propagates_to_glyphs():
+    """A z_index passed to the constructor must reach the glyph submobjects,
+    otherwise the z-ordering is ignored during rendering (see issue #4667).
+    """
+    text = Text("AB", z_index=3)
+    assert text.z_index == 3
+    assert all(glyph.z_index == 3 for glyph in text.family_members_with_points())
+
+    markup = MarkupText("AB", z_index=3)
+    assert all(glyph.z_index == 3 for glyph in markup.family_members_with_points())
+
+    # The default must remain unchanged.
+    assert all(glyph.z_index == 0 for glyph in Text("AB").family_members_with_points())
+
+
 def test_font_warnings():
     def warning_printed(font: str, **kwargs) -> bool:
         io = StringIO()