A homeless man with a “violent history” who lives at a notorious Manhattan shelter was busted for allegedly punching a Times Square Minnie Mouse in the face — but was back on the street less than 24 hours after the random attack, police and sources said.

The terrifying incident happened Friday at around 1:30 p.m., at the corner of West 42nd Street and 7th Avenue, an NYPD spokeswoman said.

The suspect, identified by cops as Donnell Smith, walked up to the costumed woman — who had Minnie’s head up, revealing her face — and allegedly socked her in the right cheek, police and law enforcement sources said.

Minutes later, cops nabbed Smith, 42, at West 42nd Street and 6th Avenue, law enforcement sources told The Post.

“He has a violent history,” an NYPD spokeswoman said of Smith, who police said has been arrested at least 15 times, ranging from petit larceny to assault to drugs to robbery to criminal contempt.

Smith, who lives at the Bellevue Men’s Shelter, at First Avenue and East 30th Street in Kip’s Bay, was charged with assault and disorderly conduct, police said.

Because the charge was third degree assault, a misdemeanor, Smith was handed a desk appearance ticket at the Midtown South Precinct on Saturday, and released from police custody, authorities said.

If a weapon was used or serious physical injury inflicted, then he would have faced a felony charge, the police spokeswoman said.

“But he punched her in the face,” she added.

The 43-year-old victim, who lives in Newark, NJ, was taken to Bellevue Hospital complaining of pain and with swelling to her face and head, authorities said.

The shelter has long been a bane to its neighbors.

Most recently, a resident there was busted in connection with the New Year’s Eve strangulation rape by a bogus deliveryman of a Kip’s Bay woman.

More than two dozen registered sex offenders currently live at the shelter, a Post analysis found.