The bodies of three adult females, an adult male, and a male toddler were found by officers responding to an 8:50 a.m. disturbance call, Sgt. Paul Chagolla told United Press International.
"All of them are family members we believe but we have not positively identified them all so we can't release any names," he said.
Chagolla said detectives were questioning a man who said he was the husband of one of the victims. "He is an investigative lead at this point," he said.
The victims were all shot, but Chagolla could not say what kind of weapon was used.
The home is located in an unincorporated area of east Mesa, a suburb of Phoenix.