The 21-year-old was substituted in Monday's 3-0 defeat at Gillingham and has now been ruled out for the rest of the season with ligament and tendon damage.
Spencer's injury means Tilson may be forced to choose from a squad of just 14 as the Shrimpers look for only their second win in 20 games.
Franck Moussa will miss out as he is serving the final game of a three-match ban,Damian Scannell (foot) is sidelined but Alan McCormack could play despite a foot problem.
The Blues will be desperate for a win at Elland Road as they look to move out of the relegation zone.
