Rafael Nadal had slipped to as low as 13th in the ATP rankings midway through 2015.
Rafael Nadal wore black ribbons during an earlier match in tribute to the victims of twin vehicle ramming attacks in Spain that left 14 dead.
Australia's Nick Kyrgios humbled new world number one Rafael Nadal 6-2, 7-5 to reach Cincinnati Masters semi-finals on Friday.
Next for Rafael Nadal, who had a first-round bye, is a third-round matchup with 24th-ranked countryman Albert Ramos-Vinolas.
Third-ranked Federer said he injured his back in Montreal, where he lost in the final to Germany's Alexander Zverev.
The Canadian teenager spoilt Rafael Nadal's chances of returning to world No 1 after defeating the Spanish great in the Montreal Masters quarter-finals.
Roger Federer attributed his renaissance to rediscovering full fitness after knee surgery in 2016 and taking a two-month break from the game earlier this year.
A semi-final run in Montreal would see the Spaniard supplant Britain's Andy Murray atop the rankings.
India's sole ATP event will be held in Pune from next year.
Roger Federer won his eighth Wimbledon crown without dropping a set.
Rafael Nadal's dramatic 6-3, 6-4, 3-6, 4-6, 15-13 fourth round defeat against Luxembourg's 16th seed Muller was his fifth exit before the quarter-finals in his last five visits to the All England Club.
Rafael Nadal dismissed Karen Khachanov in straight sets, Victoria Azarenka got the better of British hope Heather Watson in three sets.
Venus Williams wept at Wimbledon over the "devastation" of a fatal road accident for which she is facing legal action as Andy Murray and Rafael Nadal eased into the second round on Monday.
Murray will enter the tournament desperately trying to shake off a hip injury which played a part in his Queen's Club title defence coming to an abrupt end in the first round last week.
The Swiss 18-time Major champion wants to shed the 'practice world champion' tag and will be seen playing in Stuttgart this week.
Nadal beats Stan Wawrinka in straight sets to win the men's singles title at Roland Garros for the 10th time.
Simona Halep produced an incredible escape act to reach the French Open semi-finals on Wednesday.
Swiss Bacsinszky reached the women's semis for the second time at Roland Garros, to meet Latvian teen Ostapenko.