Federer suffered the problem midway through the second set of his 6-3 6-4 defeat to Alexander Zverev at the Rogers Cup in Montreal on Sunday.
It was just the third time in 38 matches this year that Federer suffered defeat.
Federer said: "I tweaked my back in Montreal and need to rest.I always enjoy playing here. Cincinnati has some of the best fans in the world and I am sorry I will miss them."
"I always enjoy playing here. Cincinnati has some of the best fans in the world and I am sorry I will miss them."
Federer's withdrawal put his participation in this month's US Open in doubt.