HPD said officers responded to the shooting at 5 p.m. at 5200 W. Alabama in the orange lot at the Galleria Mall.
The incident involved two vehicles at a halt inside the garage, where an argument between a group of males led to gunfire.
Police say that the injured man, believed to be in his 30s, was taken to a hospital in critical condition. The man, who was shot, had a small child and a woman inside his vehicle, police said.
Officials said the three detained are in their late teens to early 20s.
Details are limited as to how many shooters were at the scene.