The singer -- who's also DaBaby's ex/mother to one of his kids -- was arrested early Tuesday morning in Miami Beach ... where police claim she was involved in a DUI hit and run, which ended with a serious back injury to the alleged victim, who was riding a moped.

According to the police report, obtained by TMZ, Dani was seen by several witnesses driving at a high rate of speed and swerving in and out of lanes near Miami Beach. Eventually, cops say she struck somebody who was on a motorized scooter ... and dragged the moped for about a block. Somebody flagged down a nearby officer, who then initiated a stop.

In the paperwork, the cop describes Dani as smelling of alcohol. He conducted field sobriety tests, which he says she failed -- and says she later took a Breathalyzer.

The officer claims she blew a 0.145 and 0.148, nearly twice the legal limit. Dani was cuffed and taken to jail, where she was booked on 3 felony charges ... driving under the influence, leaving the scene of a crash with serious bodily injury, and DUI damage to property.

As for the person whom cops say was hit ... cops claim they were treated at a local hospital, where they say they were told by docs that this man suffered a kidney laceration and a spinal fracture.