Bosa suffered a calf injury ahead of Thursday's practice and was ruled out for Week 3's matchup against the Arizona Cardinals.
He is expected to miss a few weeks.
The 49ers had been considering placing Bosa on injured reserve, which would have required the star pass rusher to miss at least four weeks.
However, San Francisco has dealt with a significant number of injuries early in the season and must be selective about which players it places on injured reserve. The team can only activate eight players from injured reserve during the regular season.
The 49ers did place wide receiver Demarcus Robinson on injured reserve Saturday. Robinson suffered a high-ankle sprain in the team's Week 2 win over the Miami Dolphins but is expected to return this season.
Bosa appeared in the 49ers' first two games after returning from the ACL injury that limited him to just three games last season.
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