Russell Brand Named in Police Report -- Alleged Cell Phone Smasher

Russell Brand has been named in a police report in New Orleans ... by a paparazzo who claims the actor snatched his cell phone out of his hand and fired it through the window of a nearby building ... TMZ has learned.

Sources tell TMZ ... a photog named Timothy Jackson filed the report, citing "criminal damages" over an incident that went down Monday night.

Jackson told cops he was with a group of photogs ... when he began to shoot Brand with his iPhone from his car. Jackson claims Brand flipped out, wrestled the phone out of his hand ... and then Nolan Ryan'd it at a nearby building, shattering a glass window.

The pap immediately filed a police report. No word if he got his phone back.

Calls to Brand's rep have not been returned.

Law enforcement tells TMZ ... cops are investigating the incident and would like to speak with Brand ASAP.