One of the injured was in critical condition after the shooting yesterday in Mesa, a suburb of Phoenix, said local police spokesman Esteban Flores.
The shooter "surrendered after being tazed," said Flores, who listed at least four locations where the gunman had opened fire, before fleeing in a carjacked vehicle and being tracked down to a nearby apartment complex.
"We believe he is responsible for each and every one of these shootings," he told a briefing some five hours after the incident.
Local 12 News TV channel described the tattoos as including white supremacist symbols.
TV pictures showed the suspect being led out in a white full-body suit, designed to protect DNA and other forensic evidence for investigators who will provide evidence for prosecution.
The incident began when three people were shot at a motel. One male victim died while two women were hospitalised. Another male was shot at a nearby bistro, where a car was stolen.
"We don't know exactly what happened at the first shooting. We know there was some kind of argument," he said, adding: "We believe that he knew the first victims."
"The rest of them appeared to be carjackings or home invasions or some kinds of robberies," he said.
