They said 29-year-old Justin Colorado was taken into custody without incident Tuesday night by Navajo Nation police in northeastern Arizona and he was considered a suspect in a homicide case.
Police said 34-year-old Jessica Biakeddy of Gilbert was found lying on the ground with multiple gunshot wounds about 11 p.m. Tuesday and later was pronounced dead at a Flagstaff hospital.
A relative of the woman told police that Biakeddy was passing through town with Colorado and the two allegedly had been arguing by text messaging.
Police said they got a report about multiple gunshots being heard in an area of Flagstaff and a witness reported seeing Colorado leave the scene in a vehicle.
It was unclear Wednesday if Colorado has a lawyer yet.