Rafael Nadal celebrates a win last week at the ATP Coupe Rogers in Montreal. Photo: Getty Images
Federer, who has participated in the Ohio warm-up tournament for the US Open on seven occasions, said he had picked up the injury in Montreal, where he lost to Germany's Alexander Zverev in the final.
"I am very sorry to pull out of the Western and Southern Open as I always enjoy playing here," Federer said in a statement issued by the tournament.
"Cincinnati has some of the best fans in the world and I am sorry I will miss them. Unfortunately, I tweaked my back in Montreal and I need to rest this week."
Federer's withdrawal assures that Nadal will be top of the rankings when they are issued on August 21. The Spaniard will return to the top spot for the first time since July 6, 2014.
