Ahluwalia, who has featured in movies like "The Grand Budapest Hotel" and "Inside Man," took to Instagram to write about the incident.
"This morning in Mexico City I was told I could not board my @aeromexico flight to NYC because of my turban," he wrote.
The actor told the New York Daily News he could not remove his turban in an airport.
"That is not something that I would do in public. That's akin to asking someone to take off their clothes," he said.