Rick Ross' Rolls-Royce smashed into a building in Ft. Lauderdale, Florida early this morning ... while trying to escape from a gunman who opened fire on the car ... this according to multiple reports.

Ross was not shot during the incident -- nor was a female who was also inside the car.

According to local reports, "dozens" of shots were fired at the vehicle around 5AM -- none of which hit the Rolls. Several buildings in the area WERE struck by gunfire.

Cops say another vehicle had pulled up next to the Rolls ... when someone inside opened fire on Ross' car.

Ross' Rolls reportedly crashed into a building while trying to speed away from the gunfire.

So far, cops have not made any arrests in connection with the shooting -- and have not identified any suspects.

Local10.com obtained a photo from the crash scene, showing Ross' smashed-up Rolls-Royce being towed away.

Cops tell TMZ they are investigating.

Story developing ...