5:40 PM PT -- Pat and Marina were both released from jail and were issued temporary restraining orders to stay away from each other.

5:20 PM PT -- Kelly's attorney Alex Spiro tells us, "Pat denies all wrongdoing and will answer the charges in court."

1:55 PM PT -- Law enforcement sources tell us Pat told cops he was sleeping in his hotel room early Sunday morning when his girlfriend entered with a key he'd given her. That's when they got in the argument, at which point he says she punched him in the face, causing him to react by grabbing her by the arm and pushing her.

Former New York Yankee Pat Kelly and his girlfriend were busted in NYC over the weekend for assault ... TMZ has learned.

Law enforcement sources tell us Pat was arrested Sunday at the London Hotel in midtown along with his girlfriend, Marina Cernova.

We're told they engaged in a verbal dispute, and she punched him in the face. She told cops he grabbed her right arm and pushed her, which she says caused pain and bruising. She called cops around 2:40 AM to report Pat had beaten her.

Cops arrested and booked both of them for misdemeanor assault ... we're told they're still in jail.