Jesus Gutierrez Roman was arrested outside his Ciudad Juarez home and charged with homicide, police said.
Ciudad Juarez has been plagued by a decade-long series of more than 100 similar sexually motivated killings of young women, and it had been initially feared that Martha Vargas Jimenez's death fit that profile.
The 26-year-old had been looking for work in a maquiladora assembly plant and had been strangled, as were many of the previous victims.
However, she also suffered stab wounds, and police now believe Gutierrez Roman killed her out of jealousy.
Special prosecutor Rocio Murguia said Vargas Jimenez's body was found on Nov. 25, 2004 outside Ciudad Juarez, and had suffered physical abuse before her death, reports the AP.
NATO has no plans to deploy troops on the Ukrainian territory, Jens Stoltenberg said. French President Emmanuel Macron earlier did not rule out a possibility to send Western military forces there