Police said only that four people were shot in Mesa, a suburb of Phoenix, where SWAT teams scrambled to look for the shooter.
"We have an active shooter situation," said Mesa Police Department spokesman Esteban Flores, adding that the incident potentially involved multiple locations.
The AZ Central news website reported that the gunman shot six people, killing one.
Local schools and colleges were placed on lockdown while police searched for the victim, described as a white man in his 40s with a neck tattoo.