Wilson was kept in Little Rock, Ark., for observation following Saturday night's 34-31 overtime loss for Arkansas, which fell out of the AP's Top 25 entirely Sunday after being ranked No. 8 -- the second-biggest drop in the poll's history.
Wilson suffered the injury after taking several big hits in the first half and did not play in the second half.
"His prognosis is good," Smith said Sunday.
Wilson was 11 of 20 for 196 yards and two touchdowns against the Warhawks before leaving the game at halftime.
The first-team All-SEC quarterback also missed the second half against New Mexico last year with concussion-like symptoms.
Smith also said freshman back-up fullback Kody Walker was likely lost for the season after suffering a "lower leg injury."
And starting sophomore cornerback Tevin Mitchel remained in Little Rock after the game with "an injury above the shoulders."
Smith said Mitchel is doubtful for Saturday's game with Alabama and senior backup cornerback Kaelon Kelleybrew (bruised arm) is probable.
Brett McMurphy covers college football for ESPN.