Police said Jones, 43, got into a scuffle late Thursday at Wiley's Tavern and suffered cuts on his face from a beer glass.
A police sergeant said Jones apparently charged at Jesse Bickett of Montrose, who hit Jones with the glass.
One of Bickett's roommates, Juan Barrera, said they were playing pool when Jones asked to join, then got offended when one of them asked if he was "that guy from X-Men." Barrera said he was punched by the actor, who is mostly known for his tough guy roles, and countered with one or two of his own.
"He got offended by that, and he started pushing my other friends around," Barrera said.
Bickett, 24, was arrested on a charge of aggravated assault.
Authorities said Jones was treated at a hospital, then charged with simple assault and posted bail Friday morning.
Bickett's mother, Deb, said her son had to have surgery for his injuries.
"He (Jones) doesn't want to run into me," she said.
Jones' manager, Alex Cole, said Friday that the actor hadn't answered his phone calls. Cole had said Jones was on vacation.
Barrera said one of Jones' companions indicated he was in the state to hunt.