A worried neighbor had flagged down the officer, from the Woodbury-based Second Precinct, after seeing the loose dog "acting aggressively" near South Street and Audrey Avenue about 6:55 a.m., police said in a news release.
The officer went to the area and saw the dog attacking a woman who was walking her dog. The woman had fallen to the ground and sustained a head bruise.
The pit bull lunged at the officer, "forcing him to discharge his weapon, killing the animal," police said.
The woman, 51, was treated at a hospital for the non-life-threatening injury. A veterinarian treated her dog.
The pit bull had no tags, and police didn't immediately know where the dog came from, a police spokesman said. Town animal control staff removed its body.