Farmington police said 51-year-old Thomas Howard is facing a second-degree murder charge.
It was unclear Sunday if Howard has a lawyer yet who can speak on his behalf.
Police said officers went to do a welfare check on 65-year-old Roberta Baier on Dec. 6 after her friends reported not hearing from her in several days.
After several failed attempts to contact her, officers entered Baier’s apartment and found her dead.
Police said the death was deemed suspicious and detectives began a homicide investigation.
They said Howard was located in the Chicago suburb of Berwyn and arrested on an unrelated warrant.
Howard remains in the custody of authorities in Cook County, Illinois as he awaits extradition to New Mexico.