diff --git a/tests/test_completion/test_completion.py b/tests/test_completion/test_completion.py
index e9be4e25d1..3d4ac83217 100644
--- a/tests/test_completion/test_completion.py
+++ b/tests/test_completion/test_completion.py
@@ -119,9 +119,10 @@ def test_completion_source_zsh():
             "_TUTORIAL001_PY310.PY_COMPLETE": "source_zsh",
         },
     )
-    assert (
-        "compdef _tutorial001_py310py_completion tutorial001_py310.py" in result.stdout
-    )
+    assert "compdef _tutorial001_py310py tutorial001_py310.py" in result.stdout
+    # #1864: the function name must match the autoloaded filename (_<prog>), so
+    # it must not carry the old `_completion` suffix.
+    assert "_tutorial001_py310py_completion" not in result.stdout
 
 
 def test_completion_source_fish():
diff --git a/tests/test_completion/test_completion_install.py b/tests/test_completion/test_completion_install.py
index f6194695fe..4f9fb4aa21 100644
--- a/tests/test_completion/test_completion_install.py
+++ b/tests/test_completion/test_completion_install.py
@@ -104,10 +104,10 @@ def test_completion_install_zsh():
     assert install_source_path.is_file()
     install_content = install_source_path.read_text()
     install_source_path.unlink()
-    assert (
-        "compdef _tutorial001_py310py_completion tutorial001_py310.py"
-        in install_content
-    )
+    assert "compdef _tutorial001_py310py tutorial001_py310.py" in install_content
+    # #1864: the function name must match the autoloaded filename (_<prog>), so
+    # it must not carry the old `_completion` suffix.
+    assert "_tutorial001_py310py_completion" not in install_content
 
 
 @requires_completion_permission
diff --git a/tests/test_completion/test_completion_show.py b/tests/test_completion/test_completion_show.py
index 18f172e691..3c4b4ded03 100644
--- a/tests/test_completion/test_completion_show.py
+++ b/tests/test_completion/test_completion_show.py
@@ -68,9 +68,10 @@ def test_completion_source_zsh():
             "_TYPER_COMPLETE_TEST_DISABLE_SHELL_DETECTION": "True",
         },
     )
-    assert (
-        "compdef _tutorial001_py310py_completion tutorial001_py310.py" in result.stdout
-    )
+    assert "compdef _tutorial001_py310py tutorial001_py310.py" in result.stdout
+    # #1864: the function name must match the autoloaded filename (_<prog>), so
+    # it must not carry the old `_completion` suffix.
+    assert "_tutorial001_py310py_completion" not in result.stdout
 
 
 def test_completion_source_fish():
diff --git a/typer/_completion_classes.py b/typer/_completion_classes.py
index cfae02c9bf..802f698211 100644
--- a/typer/_completion_classes.py
+++ b/typer/_completion_classes.py
@@ -102,6 +102,10 @@ class ZshComplete(ShellComplete):
     def source_vars(self) -> dict[str, Any]:
         return {
             "complete_func": self.func_name,
+            # zsh autoloads a completion from a file named after the command
+            # (e.g. `_prog`), and the function it defines must match that
+            # filename, so drop the `_completion` suffix here. See #1864.
+            "zsh_func": self.func_name.removesuffix("_completion"),
             "autocomplete_var": self.complete_var,
             "prog_name": self.prog_name,
         }
diff --git a/typer/_completion_shared.py b/typer/_completion_shared.py
index 8d2c19715c..063aa7516c 100644
--- a/typer/_completion_shared.py
+++ b/typer/_completion_shared.py
@@ -33,11 +33,11 @@ class Shells(str, Enum):
 COMPLETION_SCRIPT_ZSH = """
 #compdef %(prog_name)s
 
-%(complete_func)s() {
+%(zsh_func)s() {
   eval $(env _TYPER_COMPLETE_ARGS="${words[1,$CURRENT]}" %(autocomplete_var)s=complete_zsh %(prog_name)s)
 }
 
-compdef %(complete_func)s %(prog_name)s
+compdef %(zsh_func)s %(prog_name)s
 """
 
 COMPLETION_SCRIPT_FISH = 'complete --command %(prog_name)s --no-files --arguments "(env %(autocomplete_var)s=complete_fish _TYPER_COMPLETE_FISH_ACTION=get-args _TYPER_COMPLETE_ARGS=(commandline -cp) %(prog_name)s)" --condition "env %(autocomplete_var)s=complete_fish _TYPER_COMPLETE_FISH_ACTION=is-args _TYPER_COMPLETE_ARGS=(commandline -cp) %(prog_name)s"'
@@ -86,6 +86,11 @@ def get_completion_script(*, prog_name: str, complete_var: str, shell: str) -> s
         script
         % {
             "complete_func": f"_{cf_name}_completion",
+            # zsh autoloads a completion from a file in $fpath named after the
+            # command (e.g. `_prog`), and the function it defines must match that
+            # filename. Use `_{name}` (not `_{name}_completion`) so the packaged
+            # / autoloaded completion actually registers. See #1864.
+            "zsh_func": f"_{cf_name}",
             "prog_name": prog_name,
             "autocomplete_var": complete_var,
         }