Hilfenhaus, who has a knee-tendon injury, had taken five wickets in the first Test, which concluded with the hosts' comprehensive an innings and 65-run win within three days.
National selection panel chairman Andrew Hilditch was disappointed on missing the services of the bowler and hoped he will recover by the third Test.
"The injury to Ben Hilfenhaus is very disappointing following his outstanding Ashes and his man-of-the-match performance in Brisbane, but hopefully with treatment he will be fit to be considered for selection for the third Test in Perth.
"It does provide an opportunity for Clint McKay to join the Australia squad for the second Test. Clint impressed all with his performances in India with the one-day squad and with his bowling for Victoria in the Weet-Bix Sheffield Shield this year," he said.
The second Test starts at the Adelaide Oval from Friday. Australia team physiotherapist Alex Kountouris admitted that workload was one of the reasons for Hilfenhaus' injury.
"Ben Hilfenhaus has had a widely-reported knee tendon injury that was sore during the recent ODI series in India and the first Test at the Gabba.
"The demands of Test cricket and the subsequent increased workload have made it harder to manage Ben's injury, so it's been decided that the best course of action is for him to miss the Adelaide Test.
"He will undergo an intense period of rehabilitation over the next two weeks with a view to him being available for selection for the third 3 mobile Test in Perth," he said.
Taylor out of series
Adding to the woes of struggling West Indies, their pace spearhead Jerome Taylor was ruled out of the ongoing Australian tour due to hip and back injuries. The Caribbean side had lost the first Test in Brisbane by an innings and 65 runs within three days.
The West Indies Cricket Board said Taylor will return home on Monday. Team manager Joel Garner the 25-year-old injured his left hip and back while bowling on the opening day of the first Test Match at the Gabba.
"He will return to Jamaica on Tuesday to continue his rehabilitation. No replacement player has been named at the moment. The team management and selectors are in the process of discussing reinforcement," a WICB statement said.
Meanwhile, middle-order batsman Ramnaresh Sarwan has been responding well to treatment for a back injury sustained ahead of the first Test, the statement added
Australia humiliate India to seal ODI series
Unpredictability reigns ahead of Guwahati ODI
Henriques ruled out of fifth ODI with injury
Rain delays start of third ODI
India slips back to third place in ODI rankings