Bradford bruised his right index finger in the fourth quarter of last Sunday's season-opening loss to the Eagles. He was a limited participant in practice on Thursday.
Bradford is listed as probable for Monday night's game with the New York Giants.
The second-year quarterback completed 17-of-30 passes for 188 yards against the Eagles before leaving.
St. Louis selected Bradford with the No. 1 overall pick in last year's NFL draft. He went on to be named offensive rookie of the year after throwing for 3,512 yards, 18 touchdowns and 15 interceptions while starting all 16 games.
Jackson departed in the first quarter. He ran for a 47-yard touchdown, but touched the ball only once more. The 28-year-old was afflicted with a strained quad in his right leg.
Amendola, the Rams' leading receiver last year, suffered his injury early in the fourth quarter on a six-yard reception.
The Rams have listed Amendola as doubtful and Jackson as questionable.