An MRI exam revealed a torn pectoral muscle that is likely to sideline him the entire season.
Immediately after Saturday's practice, coach Kyle Shanahan said Smith would probably be out for a long period, but might be able to return sometime this season.
His chances of returning this season were diminished considerably by the MRI findings, which were confirmed by the team.
In fact, NFL Network's Ian Rapoport reported that Smith will miss the entire season.
Smith joined the 49ers as a free agent in March after signing a five-year, $26.5 million deal. He played in 15 games, including 14 starts, for the Oakland Raiders last season, and he started all 16 games in 2015, when he had four sacks for the Raiders.
Smith was the MVP of the Super Bowl following the 2013 season while playing for the Seattle Seahawks
"That would be a big (loss) for us," 49ers linebacker NaVorro Bowman said, according to ESPN, before the extent of Smith's injury was known, "just because we've been getting so many reps together, jelling together and really talking about what the offense is trying to do to us throughout these OTAs and training camp. So that would be a loss, but it's early. We have other guys that I feel like can play at this level also. Let's hope not. Let's hope he's able to overcome this and get him back pretty soon."
The 49ers have not yet made a roster move to fill Smith's roster spot.
Smith, working as the starting weak-side linebacker, was injured while running down running back Matt Breida. Smith appeared to get his arm caught on Breida's helmet.
Rookie Reuben Foster or Ray-Ray Armstrong is likely to replace Smith as the starter.