The 27-year-old was taken to hospital after the incident around 10.15pm last night (Wednesday).
The victim ran into the restaurant for help after the late night assault and collapsed on the floor.
He is believed to have been bleeding heavily.
Police are appealing for information.
A Police Scotland spokesperson said: “We received a report of an assault on Torbrex Road, Cumbernauld around 9.55pm on Wednesday 30 October 2019.
“A 27-year-old man was taken to Monklands Hospital with facial injuries and has since been released.
“Enquiries are ongoing to establish the full circumstances. If anyone has any information about this incident please contact us on 101 quoting incident number 3919 of 30 October or anonymously via Crimestoppers on 0800 555 111.”