Norton's left arm had to be amputated by paramedics at the scene, his agent confirmed in a statement.
The 22-year-old Norton is in critical condition but is expected to live, sources told Omar Kelly of the South Florida Sun-Sentinel.
"We were made aware this morning of a serious car accident involving Kendrick Norton. Our thoughts and prayers are with Kendrick and his family during this time," the Dolphins said in a statement.
The Dolphins claimed Norton - who attended the University of Miami - off the Carolina Panthers' practice squad in 2018. He never played an NFL snap.
Carolina selected Norton in the seventh round of the 2018 NFL Draft.