Investigators arrived at the 7500 block of Harwin Road near Fondren and found one person dead from a gunshot wound in the strip center's parking lot.
Asst. Chief Yasar Bashir of HPD said it was just after 6:30 a.m. when the suspect reportedly came to the location and shot the victim, who was on the clock, multiple times before calling the police.
Police said both security guards knew each other and worked for the same company, but what led up to the shooting remains unclear.
According to officials, the suspect and the victim are men in their 60s.
A weapon was recovered amid the investigation, and the suspect was detained at the scene.