Rudolph left Week 12's loss against the Bears after getting drilled by linebacker Lance Briggs on a third-down play in the red zone. While Rudolph was cleared for the concussion, the tight end was expected to miss Wednesday's practice because of a shoulder strain.
Smith suffered his concussion after knocking Bears wide receiver Earl Bennett out of bounds in the third quarter. Smith said he actually passed a concussion test after the game, but that he was held out for precautionary reasons. The safety also suffered a concussion back in 2008 at Notre Dame.
Star running back Adrian Peterson may be limited in practice as he recovers from a shoulder strain suffered in the loss to the Bears.
Minnesota faces the Green Bay Packers this Sunday.