Chief Chuck Hasty said the call came in as a dog running at large around 4:45 p.m.
When Officer D. Daniels arrived, Hasty said the officer observed the dog attacking the child.
The dog was aggressive and was shot, Hasty said.
The child was bitten on the extremities. A condition was not immediately available.
Police and city Animal Control Officer Pete Wilson are investigating to determine ownership and whether charges will be filed.