Hazlewood,who played in the opening four Ashes Tests, will miss the dead-rubber at The Oval due to 'niggling' injury problems.
His withdrawal will likey see fellow New South Welshman Cummins make his long-awaited return to the Test arena.
The 22-year-old played his one-and-only Test against South Africa as a teenager in 2011.
He took seven wickets and hit the winning run in a stunning performance before a string of serious injuries halted his meteoric rise.
Coach Darren Lehmann did not reveal Hazlewood's replacement but Cummins is all-but certain to be unleashed in the Ashes finale.
"Josh has played six Tests since the West Indies Tour and the last nine Tests for Australia, as well as playing an important part in the World Cup," Lehmann said.
"He has managed to get through this period without any major injury which is pleasing, though currently he does have some niggling problems that we would like to manage. As such, he was not considered for selection for the fifth Test.
"On his return to Australia his niggles will be investigated further and he will work with our coaches and our medical and fitness staff to have him prepared for the next series he is selected to play in."
England regained the Ashes at Trent Bridge as a crushing innings and 78-run victory gave Alastair Cook's side an unassailable 3-1 lead.