Crutchlow had been fifth fastest in the morning session but suffered a heavy fall in the afternoon, fracturing his right ankle and tibia.
"After being seen by medics at the track, the 32-year-old was taken to Melbourne Alfred City Hospital where he will undergo surgery to correct the injury," the team said.
Australian Grand Prix
Injured Crutchlow undergoes second operation
01/11/2018 AT 09:10
Crutchlow, a three-times winner in motorcycling's top category, had finished second at the previous round in Japan, a race that saw Spaniard Marc Marquez take his fifth MotoGP championship.
The Briton is fifth in the overall standings with two races remaining after Australia.
Ducati's Jorge Lorenzo will also be absent from Sunday's race as he recovers from recent wrist surgery in Spain.
Australian Grand Prix
Iannone tops FP2, Crutchlow in heavy crash
26/10/2018 AT 06:58
Australian Grand Prix
Lorenzo to miss Australian GP as well
21/10/2018 AT 06:06