Pinal County Sheriff's officials say 52-year-old Joseph Terrigino is being held on suspicion of one count of felony second-degree murder without premeditation.
The body of 40-year-old Diane McQuiston was found in Apache Junction by a water company worker in October 1988.
The county medical examiner determined McQuiston died of multiple gunshot wounds.
Apache Junction police say the the department's Cold Case Unit began reviewing the case last November.
A county grand jury indicted Terrigino and an arrest warrant was issued in February.
Authorities say he was arrested last month near Hardin County in Kentucky and extradited to Arizona.
It was unclear Monday if he has lawyer.