EXCLUSIVE

The NYPD is investigating J.R. Smith for allegedly stealing a cell phone from a fan and throwing into a construction site ... TMZ Sports has learned.

Law enforcement sources tell us ... they got a call around 2:30 AM on Sunday morning from a guy who says he tried to take a picture with the Cleveland Cavs star outside of The Park, a hot spot in Chelsea.

Smith allegedly turned the fan down -- telling him no photos -- but he snapped one anyway ... and Smith snapped too.

We're told ... Smith allegedly approached the fan and snatched the phone out of his hand and then launched it into a nearby construction zone. The fan claims his $800 phone was damaged and he has filed a report with police.

Smith has not been charged with a crime -- but we're told cops would like to speak with him asap.

We talked to J.R.'s attorney, Alex Spiro, who vehemently denies the allegations ... saying, "the claim is nonsense and we do not have anything to say about nonsense."