Kennedy copped a heavy knock to his face in a marking contest late in the 38-point loss to North Melbourne on Sunday night.
It was believed he had just received a black eye and would be right to play this week, however scans have confirmed that he has suffered a depressed fracture of the cheekbone and will need surgery.
Kennedy will not fly to Launceston to face the Hawks but the club is hopeful he could be fit to face Gold Coast in round 13.
The 26-year-old Eagles vice-captain has kicked 25 goals this year including a bag of 11 against Greater Western Sydney in round eight.
The Eagles also have concerns over the fitness of Xavier Ellis (corked hamstring) and Brad Sheppard (corked buttock). Both will be given until later in the week to prove their fitness for the vital match with the Hawks.
