Two of the injured are reported to be in a critical condition, Austin Police Department Interim Chief Joseph Chacon said in a statement.
The incident took place at around 01:30 am in the Sixth Street Entertainment District area and there were no deaths reported at the time of the briefing, he added.
"It's not clear at this point what sparked this off, but out of an abundance of caution, we have notified the FBI's joint terrorism task force," Chacon said.