On Wednesday, the 12-year veteran said about 50 percent of his left triceps tendon was torn, according to Comcast SportsNet Bay Area.
NFL.com's Ian Rapoport had reported earlier this week that Smith would have surgery on the arm a few days after the season.
"I'm not going to retire after this year," Smith said. "I would like to come back and try to get here (the Super Bowl) again. I realize my career is definitely winding down. I'm not saying I'm going to play another eight years or something like that. I want to play at a high level."