The two injured victims whose identities were unknown were rushed by security officials to Thammasat hospital for medical treatment.
A witness told police that he heard gunshots and then saw a man holding a pistol run out of the race course toward a car and then drove away.
Police combed the area where the gun was suspected to fire into the crowd and found four spent shells of 9mm ammunition.
They have also asked cooperation from factories located near the race course for footages from their surveillance cameras which may provide police with a clue about the car driven by the gunman which may track to the gunman.
Police suspected that the shooting might stem from conflict between race course operators or conflict between rival groups among the spectators.