The mother and child were among 2,000 fans at the USA Stadium in Millington that night, attending the University of Memphis' baseball game against the University of Tennessee at Martin during the annual W.S. "Babe" Howard Classic.
The child had been playing in a vintage World War II jeep on display at the stadium as part of a Veterans Appreciation Day, according to the Millington Police Department.
The child found an unsecured handgun inside the vehicle and thought it was a toy. The child picked up the gun and pulled the trigger, firing a round that struck the mother, police said.
Officers received a call about shots fired just before 6:30 p.m. local time.
The mother was taken to a local hospital in critical condition, police said.
The baseball game was suspended due to the incident.
Police declined to release the names of the mother and child.
Investigators later determined that the unsecured gun belonged to 76-year-old Charles McFarland, who was subsequently charged with reckless endangerment with a deadly weapon. No bond has been set at this time, police said.