'Hangover' Actress Nathalie Fay Arrested For Domestic Battery

Nathalie Fay , an actress with a memorable part in the first 'Hangover' film, has been arrested for allegedly punching her boyfriend in the face ... TMZ has learned.

The actress -- whose real name is Nathalie Tordion -- was arrested in South Miami, Florida on Saturday after police responded to a call about an incident with her on-again, off-again BF, identified in the police report as Brady .

Cops say Brady told them he'd gone to pick up Nathalie for the Miami Dolphins NFL preseason game against the Washington Commanders.

When he arrived to pick up Nathalie, Brady claims she hopped in the car and began asking where he'd been prior to picking her up ... allegedly showing him a map to prove he wasn't where he said he'd been.

While Brady looked at the phone, he says Nathalie punched him square in the face ... at which time, Brady says, he got out of the car to get away from Nathalie.

Police came to the scene and arrested Nathalie for domestic battery. Brady refused transport to a hospital and advised he would go on his own.

Fay's appeared in some classic comedy flicks during her career, including "Old School," "Due Date," "Blonde and Blonder" and more.

She's probably best known as the hotel desk attendant who greets Bradley Cooper , Ed Helms and company when they arrive at Caesar's Palace in "The Hangover" ... answering Zach Galifianakis ' character's question about Julius Caesar .

We've reached out to Nathalie, who declined to comment on this story.