Sources told ESPN it is believed that Brennan has a broken arm. A timeline for his return is unclear.
Brennan began last season as the starter, throwing for 11 touchdowns in three games before an abdominal injury ended his season.
A fourth-year junior, Brennan said earlier this offseason that he was feeling 100 percent again. He was expected to compete for the starting job against Max Johnson.
Johnson, the son of former NFL quarterback Brad Johnson, came on late last season as a freshman, leading LSU to a 2-0 record.
At SEC media days last month, coach Ed Orgeron said he thought that Johnson and Brennan were “championship quarterbacks.”
“Whoever wins is going to do a great job at LSU,” Orgeron said. “It’s going to be a tremendous battle, and we’ll see what happens.”
LSU is scheduled to open the season at UCLA on Sept. 4.