One of Floyd Mayweather's giant TMT members roughed up a fan as the boxer left a famous chicken joint in Hollywood -- and now police are involved ... TMZ Sports has learned.

It all went down outside the legendary Roscoe's House of Chicken and Waffles on Wednesday evening -- where Floyd and his massive TMT entourage had dinner around 8 PM.

On his way out, Floyd was approached by a 20-year-old man in a white shirt and glasses who asked Floyd and his crew if he could take a quick photo.

That's when one of Floyd's guys -- a big dude in a red shirt -- rushed to the fan, grabbed him by the neck and slammed him against a wall.

(FYI, that same TMT entourage member was with Floyd during a shopping trip in Bev Hills earlier in the day and was sure acting like a member of the security team). 

THE ALLEGED PERP
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After the video ends, we're told Floyd's crew put the boxer in the car and bolted.

The man -- who claims he was also punched in the face -- filed a police report and told cops he suffered injuries to his head, neck and mouth.

We spoke to the victim who says he is (was) a HUGE Floyd fan and just wanted a pic -- he wasn't trying to start any trouble.

Sources connected to Floyd's camp tell us the man in the red shirt is "not on the payroll" -- he's just with the entourage.