diff --git a/Lib/fontTools/ttLib/reorderGlyphs.py b/Lib/fontTools/ttLib/reorderGlyphs.py
index 3221261f1..0e4a99fc1 100644
--- a/Lib/fontTools/ttLib/reorderGlyphs.py
+++ b/Lib/fontTools/ttLib/reorderGlyphs.py
@@ -258,6 +258,12 @@ def reorderGlyphs(font: ttLib.TTFont, new_glyph_order: List[str]):
             f"* only in old: {set(old_glyph_order) - set(new_glyph_order)}"
         )
 
+    # Glyph 0 must be assigned to a .notdef glyph.
+    # https://learn.microsoft.com/en-us/typography/opentype/spec/recom#glyph-0-the-notdef-glyph
+    if ".notdef" in new_glyph_order:
+        new_glyph_order.remove(".notdef")
+        new_glyph_order.insert(0, ".notdef")
+
     # Changing the order of glyphs in a TTFont requires that all tables that use
     # glyph indexes have been fully.
     # Cf. https://github.com/fonttools/fonttools/issues/2060
@@ -276,3 +282,11 @@ def reorderGlyphs(font: ttLib.TTFont, new_glyph_order: List[str]):
                 reorder_key = (type(value), getattr(value, "Format", None))
                 for reorder in _REORDER_RULES.get(reorder_key, []):
                     reorder.apply(font, value)
+
+    if "CFF " in font:
+        cff_table = font["CFF "]
+        charstrings = cff_table.cff.topDictIndex[0].CharStrings.charStrings
+        cff_table.cff.topDictIndex[0].charset = new_glyph_order
+        cff_table.cff.topDictIndex[0].CharStrings.charStrings = {
+            k: charstrings.get(k) for k in new_glyph_order
+        }