The Egypt skipper was subjected to a tough challenge from a Beerschot defender seven minutes before the break.
Hassan was replaced at halftime after failing to play through pain.
"I suffer a severe back pain. I will undergo a scan on Thursday to determine the extent of the injury," the 32-year-old midfielder told FilGoal.com.
"I hope that my bone wasn't fractured because such an injury will rule me out for the rest of the season."
Anderlecht, whose hopes to defend their Belgian League title faded, advanced to the Cup final with a 6-2 aggregate win over Beerschot. They will face Gent in the tournament's finale.
Hassan recently said that he dreams of lifting the cup to end his three-year spell with Anderlecht on a high note.
The former Besiktas man has agreed a deal to join Egyptian champions Ahli next season to end a ten-year stint in European football.