The Houston Police Department said the deadly shooting happened in the 3400 block of Blalock Road.
Video shows the suspect on the ground and handcuffed after his arrest.
Investigators say neighbors heard gunfire and found the victim shot in the driveway.
Officers said they spotted the suspect, who then ran into a neighborhood on Campbell Road. HPD canines helped sniff out the suspect about two miles from the scene.
Lt. Larry Crowson said the suspect was injured, having "canine contact," and he is expected to be OK.
A motive has not yet been released.
If you know anything about this case, authorities urge you to contact the Houston Police Department's Homicide Division at (713) 308-3600.