The unidentified man approached three children between the ages of 5 and 7 near a trash bin around 5 p.m. on Feb. 28, according to the Dallas Police Department.
The man then pulled out a gun and shot the dog in the face, investigators said. The dog survived but suffered a "major injury to his mouth."
It's unclear why the man shot the children's dog, identified by WFAA as Nolan, a 9-year-old Labrador Retriever owned by Genola Vance.
Vance said she'd asked her son and nephews to take out the garbage on the day of the shooting, and soon afterward the kids shouted, "Someone shot Nolan!"
"They said he just looked at them, said 'Sorry,' and then shot him," Vance told the news station. "He ran by me into the house and there was blood everywhere."
Nolan underwent emergency surgery at an animal hospital for a broken jaw. Veterinarians, according to WFAA, placed an external fixator on the dog's jaw to hold it in place.
SPCA-Dallas reportedly paid for the medical procedure, which was said to have cost around $7,000.
Vance claimed Nolan, whom she adopted last year, followed the children outside for a purpose.
"I think if Nolan wouldn't have run outside, maybe this man would have shot one of the kids," she said. "He took a bullet for my family."
Anyone with information related to the shooting is urged to contact Crime Stoppers or the Dallas Police Department's Animal Cruelty Unit.