A neighbor reported the fire around 3 a.m. Friday.
Police tell KIFI-TV that two women and two children died in the house. A man was found alive but later died at Eastern Idaho Medical Center. The victims' names and causes of death have not been released.
Officials say the small fire started in the basement and only damaged the stairwell.
Ammon is a city of about 12,000 just east of Idaho Falls.
Information from: KIFI-TV