Steve Buscemi's alleged attacker has been arrested in NYC -- and cops say they picked him up after responding to a call at a homeless shelter ... TMZ has confirmed.

Law enforcement sources tell TMZ ... Clifton Williams -- the man police believe is the guy who walked up to the actor and punched him in broad daylight -- was taken into custody Friday after cops responded to a harassment call at a homeless shelter in Manhattan.

We're told cops say Clifton started making a lost property police report and showed officers ID ... when they recognized his name and then took him into custody. The NY Post broke the news first.

As we reported ... Buscemi was walking down the street in the Kips Bay neighborhood on Manhattan's east side when he says a dude stepped up and clocked him. Surveillance video shows SB walking around before the incident but does not show any violent encounter.

Photos of bruising around Buscemi's eye surfaced in recent days, but he released a statement Sunday letting his fans know he's doing alright and recovering.

New York's been plagued by random acts of violence in recent months ... including a couple other incidents involving celebs in the city.

We're told Clifton's currently awaiting charges and has not yet been released.