He broke his nose after collision with an Al Rayyan player in Doha last week.
Alishah will be ruled out for between four and five weeks.
Persepolis will meet Al Shorta in a must-win game on Matchday six of the 2024-25 AFC Champions League Elite in Doha.
The Iranian side sits ninth in the 12-team table, while the eight top teams will qualify for the next stage.