Reid said that Smith's shoulder "is a little tender," and that the injury occurred late in the first half of Sunday's win over the Rams. Smith continued playing and completed 24-of-28 passes for 226 yards in the game.
The Chiefs carry two other quarterbacks on their roster: Chase Daniels and rookie Aaron Murray.
Smith, 30, was 11-4 as the Chiefs' starter last season, with a career-high 23 passing touchdowns.
Kansas City is 4-3 this season and plays the Jets at home in Week 9.
- Josh Sanchez