Police say the car then sped off.
Investigators are seeking the parents of the boy, whose umbilical cord was still attached when he was found by a woman passer-by. Doctors believe the infant was less than an hour old at the time.
Sheriff's spokesman Jim Leljedal said the woman brought the infant to the sheriff's office. The baby was taken to Broward General Medical Center, which upgraded his condition from critical to serious Thursday night.
It was unclear what injuries the eight-pound, two-ounce child may have suffered.
The woman who rescued the baby - who was inside a small plastic bag - said she saw a man and woman arguing inside the vehicle.
The baby was thrown from the passenger side, landing three or four feet away in the grass.