With the World Cup starting in South Africa in February, Australia's selectors have decided to rest the lanky paceman from the upcoming matches with England and Sri Lanka.
Adam Gilchrist, who has been promoted to the captaincy after Ricky Ponting was given the game off, said McGrath was expected to return in time for the first one-day final on Thursday.
"It's more precautionary than anything," Gilchrist said.
"He just wants to make sure that he can really get rid of this niggle and make sure he's fresh for the finals and obviously the big workload after that."
Brett Lee has been recalled as McGrath's replacement for Australia's match against England on Sunday after initially being told he could have a rest.
Middle-order batsman Michael Clarke has also been added to the team to make his international debut after Darren Lehmann was suspended for his racial outburst in the match against Sri Lanka.
With Australia already assured of a place in the triangular one-day finals, the selectors have decided to rest several key players and save them for the World Cup.
Paceman Jason Gillespie has not played since the final Ashes test in Sydney after injuring his elbow but is almost ready to make a comeback after training on Saturday.
"He had a light trundle this morning and it's great to see him back," Gilchrist said.
"He had a really positive outlook on it and obviously he is keen to get back in as soon as he can."