Henry Guler-Romero was taken by 22-year-old Mesut Guler from an apartment complex around 4 p.m. Tuesday.
Guler allegedly got into an argument with the baby's mother and fled with the infant, claiming he was leaving the state. He told her through a text message he could harm himself and their child.
"Anybody that threatens their child, I would say, is a credible threat, and anybody's capable of doing anything," said Capt. Dave Pitts with the Sunnyvale Police Department.
A "ping" from the suspect's cellphone was tracked near the 805 Freeway and Balboa Avenue in the community of Kearny Mesa in San Diego at 11:55 p.m. Tuesday.
Within hours, two reports of unconfirmed sightings of his vehicle were also reported.
Guler was reportedly stopped at a checkpoint in Mexico and questioned by Mexican authorities. The Mexican authorities then contacted U. S. Border Patrol Agents in Lukeville, Ariz.