Police Lt. David White said the officer, whose name wasn't immediately released, was taken to South Baldwin Regional Medical Center Friday night.
It was not immediately clear how serious his injuries were.
White said the officer pulled over Anthony Lee Taylor just after 7 p.m. Friday.
Taylor fled after the officer found narcotics in the car.
The officer was dragged a short distance as he tried to prevent Taylor from getting away.
White said Taylor was eventually stopped in the Bon Secour area.
Police say a 5-year-old and the child's mother were also in the car.
(Copyright 2009 by The Associated Press. All Rights Reserved.)