The shooting occurred after police tried to stop a Ford Mustang at about 1 a.m., said Trent Crump, a spokesman for the Phoenix Police Department.
The car initially eluded the officers, who found it a short time later. Police were looking for the occupants of the car when shots were fired, wounding Officer Travis Murphy, 29, The Arizona Republic reported.
Officers rushed Murphy to a hospital in a police car. He was pronounced dead at about 3:30.
A tactical team with a police dog found a suspect, Danny Martinez, police said. Martinez, naked, was hiding in a shed.
Police Chief Jack Harris left a meeting in Washington with U.S. Attorney General Eric Holder and returned to Phoenix after getting news of the killing, KPHO-TV, Phoenix, reported.
"One of the first things that his wife said to me was that he absolutely loved his job. And he absolutely loved our department." Harris said. "She said she asked him if he wanted to get promoted in the future or work a specialty detail. He said he wanted to do just what he was doing."
Murphy and his wife have two young children, a girl, 2, and a boy born two weeks ago.
The Arizona Department of Corrections said Martinez was freed in 2009 after serving time for a weapons charge.