Police say 49-year-old Carlos Urias assaulted the woman, Joanne Otero, and she later died from traumatic injuries to her chest.
The assault happened in the area of 4th and G Street late in the night on December 23.
Police believe Otero was looking for a place to sleep when she was brutally attacked by Urias.
Detectives worked through Christmas and identified Urias through footage from nearby security cameras.
Urias was found and arrested on Friday, and booked into the Madera County Department of Corrections on the charge of murder.