'Hangover' Actress Nathalie Fay Hit With Restraining Order After Arrest

"Hangover" actress Nathalie Fay is now required to keep her distance from her on-again, off-again boyfriend William Brady ... as she's been hit with a restraining order.

TMZ broke the story ... when the actress -- whose real name is Nathalie Tordion -- was arrested in South Miami, Florida for allegedly punching Brady in the face.

William now wants Nathalie to steer clear of him ... new court documents show she's been ordered to stay at least 500 feet away from her beau, and she's not to contact him through writing, social media, calls -- or any other form of communication.

However, Nathalie is allowed to return to the house she shares with William to gather her belongings ... but will require a police escort if she does.

If she doesn't have an officer with her when she goes back, she could be arrested again.

Nathalie -- best known for playing the Caesar's Palace hotel concierge in the first 'Hangover' film -- has appeared in a number of big-screen comedies, such as "Old School," "Due Date," and "Blonde and Blonder," among others. Her arrest, however, is no laughing matter.

As TMZ previously reported ... police arrested Nathalie for domestic battery after William alleged she punched him in the face while arguing in a car.

Brady, who had picked Nathalie up for a Miami Dolphins NFL preseason game, claimed Nathalie was suspicious about his whereabouts earlier in the day ... and he told cops the conversation took a violent turn.