San Antonio Police Chief William McManus said the search had intensified for the suspect, who they believed was seen in surveillance video released to the public.
Detective Benjamin Marconi, 50, was killed late Sunday morning.
Possible confession from San Antonio suspect
Police said Otis Tyrone McKane, 31, was arrested around 4:45pm Monday in San Antonio.
While being walked out of the police department, McKane said he had gone through several custody battles and "lashed out at someone who didn't deserve it."
When asked if he had anything to say to the family, he said, "I'm sorry."
Police said they were watching McKane for some time before stopping him and arresting him near San Antonio. A woman and a 2-year-old child were with him in the car, police said.
Chief McManus says Marconi had pulled over a vehicle and while he was inside his vehicle writing a ticket, a vehicle pulled up behind him. The driver of that vehicle got out, walked up to the officer's driver-side window and shot the officer in the head, police say.
Police released a photo of a person seen on surveillance video at the time of the crime.
McManus said, "I think that the uniform was the target, and anyone who happened along was the person he targeted."