Lt. Scott Walton says the shooting took place Wednesday morning at a Bank of America branch as the suspect struggled with the guard.
Walton says the suspect then ran from the scene and confronted two people, demanding the keys to a vehicle. Officers arrived and arrested the suspect before he could drive away.
The guard has been transported to a Dallas hospital. Walton had no immediate information on his condition. The guard's name has not been released.
Police did not immediately provide further details.