Smith was lifted from the game during a commercial break in the second period. Just before that, he was slow to get up after a collision with teammate Devon Shore, who was backchecking hard to defend a Ducks offensive chance in the slot.
Smith did not join his teammates on the bench to start the third period. Mikko Koskinen replaced him in goal for the Oilers.
After the game, head coach Dave Tippett said Smith tweaked something and removed himself from the game as a precaution. He is considered day-to-day with a lower-body injury and will be evaluated on Wednesday.
If Smith is unavailable for the team's upcoming road trip, Stuart Skinner could be recalled from AHL Bakersfield to backup Koskinen.
The 39-year-old Smith had a 21-6-2 record with a 2.31 goals-against average and .923 save percentage last season, his best campaign in nearly a decade. The performance earned the native of Kingston, Ont., a new two-year, $4.4-million contract with Edmonton and the team is counting on him to maintain that form so it can stay in the playoff race.