Brooks was seen by police getting off a motorcycle and running into the Eastfield Plaza Apartment complex around 11:30 a.m. Tuesday.
Investigators say Brooks was staying at the nearby Mesquite Inn, just west of the current search area, before he fled into the apartment complex.
Police requested K-9 units and assistance from the Mesquite police department. FBI agents also went to the apartment complex to search for the suspect.
K-9 units were on the scene for about an hour and a half. During that time, the dog led police outside the complex to a nearby creek bed, then into an area filled with trees.
The FBI arrested a man who caused a Dallas apartment complex to be locked down for several hours Tuesday after he fled when authorities tried to serve a drug warrant.
A bureau spokesman said 41-year-old Ronald William Brooks was apprehended in the Dallas suburb of Mesquite without injury Tuesday night.