6:25 PM PT -- The suspect's been booked for felony assault, because Rudy is over 65 years old.
Rudy Giuliani was allegedly the subject of a physical assault while out shopping in New York, TMZ has learned.
Law enforcement sources tell TMZ ... Giuliani was at a ShopRite store in Staten Island Sunday after helping campaign for his son, Andrew Giuliani, when an employee allegedly came up to him, smacked him hard on the back, and said "What's up, scumbag?"
We're told cops arrived and took the 39-year-old suspect into custody, who was on the clock at the time. Giuliani refused medical attention.
Police are still investigating and interviewing witnesses ... cops say some were shocked by what went down.
Andrew told the New York Post his dad is doing fine now ... adding, "It’s a sad day when New Yorkers' greatest crime fighter, 'America’s Mayor,' is attacked. I blame the left-wing for encouraging violence. This is crazy."