Officers and medics responded to the 3900 block of S. 12th Street at about 10:30 p.m. Friday after receiving a report of a hit-and-run accident.
Arriving at the scene, a pedestrian was found with life-threatening injuries and was taken to the hospital.
Police learned that the driver had fled on foot. A K-9 police dog was brought in but it could not pick up the suspect's track, said Tacoma police spokeswoman Loretta Cool.
Officers later were able to identify the suspect but still had not yet located the person as of mid-afternoon on Saturday, Cool said.
The age, gender and hometown of the victim were not immediately available.