According to police, officers responded to a shooting near the AT&T location at 3329 Oak Lawn Avenue shortly after 10 a.m.
The person who called police said someone ran up to him and threatened to kill him, said Melinda Gutierrez, Dallas police spokeswoman. The caller, who is a concealed handgun owner, shot and killed the person, Gutierrez said.
Nearly one dozen police patrol cars were seen outside the store, along with one Dallas Fire-Rescue ambulance.
One person was seen detained in the back seat of a police cruiser. Neither of the people involved have been identified and police have not said if the man who shot the other will face any charges.
The investigation into the shooting is ongoing.