The Scot has been suffering from the problem for a sustained period and has decided it would be best if he missed the upcoming tournament in NY.
After missing the second half of last season with a knee problem, Federer has won five titles this year, including the Australian Open and Wimbledon trophies.
"Was actually practicing okay the last few days, but it's too sore for me to win the tournament and ultimately that's what I was here to try and do", he added.
Former world number one Roger Federer, who had been blessed with a body that seemed bullet-proof against the aches, pains and injuries suffered by most top athletes, is in the midst of one of the greatest ever comebacks from injury.
The fourth stage of the season of Grand Slam tennis begins Monday in NY.
The 22-year-old, who arrived in NY on Saturday after reaching the semifinals of the Winston-Salem Open, said: "It's just unfortunate Andy's not playing but it doesn't change how I approach it".
Murray - who has been struggling with the injury since before Wimbledon - announced the decision on Saturday, just two days before the tournament begins.
Chelsea loan out Boga as Oxlade-Chamberlain talk builds
But, a constant shuffling of positions and injury troubles at Arsenal have seen the player make little progress in his career. Oxlade-Chamberlain has made 198 appearances for the Gunners since joining them from Southampton in August 2011.
Murray said: "I certainly wouldn't have been hurting myself more by trying to play".
"Every injury has its complications and you can go and see a number of different specialists and you might get quite varying responses in terms of next steps, best steps".
The question now is if Murray will play at all the rest of the season.
"Obviously I spoke to a number of specialists about it to get the best advice possible", Murray noted.
Kathleen Stroia, the WTA's Senior Vice President of Sport Sciences & Medicine and Transitions, said the schedule's setup helps players limit changes in court surfaces but they must still plan accordingly for the transitions.
"But obviously I'll need to make the correct decision and really think it through these next couple of days with my team".
The lucky loser is Lukas Lacko (that nearly rhymes).
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