The openside flanker had been hoping to benefit from the absence of David Pocock, who is on a year-long sabbatical, to get some test game-time as backup to Michael Hooper when Australia host Fiji, Scotland and Italy in June.
The 15-cap Wallaby was, however, taken to hospital after injuring his wrist in a tackle during the heavy loss to the Canterbury Crusaders on Saturday.
"McMahon was cleared of any fractures but required a procedure to relocate his wrist," the Rebels said in a statement on Sunday.
"The 22-year-old was discharged from hospital on Sunday morning and is expected to miss 6-8 weeks."
Rebels coach Tony McGahan suggested McMahon's back-up, Colby Faingaa would be a suitable replacement in Michael Cheika's squad but the injury might open the door for an unlikely comeback for 36-year-old George Smith.
Smith, who won the last of his 111 caps in the 2013 British and Irish Lions series, has been playing well for the Queensland Reds and said last week he would be delighted to play for Australia again if "everyone fell down".
With Liam Gill playing in Toulon and therefore ineligible, Smith's Reds team mate Adam Korczyk and Western Force flanker Richard Hardwick are the other young guns most likely to get a call-up.
(Reporting by Nick Mulvenney, editing by Amlan Chakraborty)
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