diff --git a/cibuildwheel/oci_container.py b/cibuildwheel/oci_container.py
index 1ea22edd9..71c30f1cd 100644
--- a/cibuildwheel/oci_container.py
+++ b/cibuildwheel/oci_container.py
@@ -17,7 +17,7 @@
 from typing import IO, Dict, Literal
 
 from .typing import PathOrStr, PopenBytes
-from .util import CIProvider, detect_ci_provider, parse_key_value_string
+from .util import CIProvider, call, detect_ci_provider, parse_key_value_string
 
 ContainerEngineName = Literal["docker", "podman"]
 
@@ -108,7 +108,16 @@ def __enter__(self) -> OCIContainer:
         if detect_ci_provider() == CIProvider.travis_ci and platform.machine() == "ppc64le":
             network_args = ["--network=host"]
 
-        shell_args = ["linux32", "/bin/bash"] if self.simulate_32_bit else ["/bin/bash"]
+        simulate_32_bit = self.simulate_32_bit
+        container_machine = call(
+            self.engine.name, "run", "--rm", self.image, "uname", "-m", capture_stdout=True
+        ).strip()
+        if container_machine not in {"x86_64", "aarch64"}:
+            # either the architecture running the image is already the right one
+            # or the image entrypoint took care of this
+            simulate_32_bit = False
+
+        shell_args = ["linux32", "/bin/bash"] if simulate_32_bit else ["/bin/bash"]
 
         subprocess.run(
             [