San Antonio Police Chief William McManus told an early morning news briefing that a group of people were denied entry to the bar around midnight.
The shooter said, "'don't you know who I am? I'm a UFC fighter from California,'" according to McManus.
A man in the group went to a vehicle, got a rifle, walked across the street and started shooting people, McManus said.
The gunman fled the scene.
Police said that the victims included five women and three men, between the ages of 23 to 41. All were listed in stable conditions at local hospitals, police said. Neither the alleged shooter nor the victims were identified.
Few other details were immediately available. Calls to the San Antonio police representatives seeking more details were not immediately returned early Saturday.
There have been numerous mass shooting in the United States recently, including a shooting outside a Walmart at the border town El Paso in August 2019, that left 22 people dead.