The Swiss, a record 19-time grand slam champion, was the only player who could have prevented Nadal reclaiming top spot from the current number one, Andy Murray.
Federer suffered an injury last weekend during his defeat in the Rogers Cup final in Montreal to rising German star Alexander Zverev.
Murray has already pulled out of Cincinnati – one of the main warm-up tournaments ahead of the US Open, which begins this year on Monday August 28th.
Nadal is back at the summit of men’s tennis for the first time since July 2014. The 31-year-old Spaniard recently claimed his tenth French Open title.
On his Cincinnati withdrawal, Federer said:
“I am very sorry to pull out. 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 need to rest this week.”