The Swiss ran out a 6-1 6-2 winner to set up a match with world number 24 Jerzy Janowicz who beat ninth seed Richard Gasquet 3-6 7-6 (7/2) 6-4.
Federer needed just 23 minutes to win the first set against Simon, making use of all three of his break points and was never troubled on serve as he clinched the emphatic win in an hour and two minutes.
Rafael Nadal recovered from a nightmare first set to edge past Latvian qualifier Ernests Gulbis 1-6 7-5 6-4 in two hours and 37 minutes.
"I thought I was the better player in the match and also in the second and third sets but he is the champion," said Gulbis who raced into a 5-0 lead in the first set.. "I lost against him in Indian Wells when I also thought I played better than him. He is solid and he didn't do anything special and I made mistakes and so he won."
Nadal will play compatriot David Ferrer in the last eight after the Spaniard was given a walkover against injured opponent Philipp Kohlschreiber.
Earlier top seed and world number one Novak Djokovic found the going easier against Ukraine's Alexandr Dolgopolov, holding serve throughout and breaking three times for a straightforward 6-1 6-4 success.
Sixth seed Tomas Berdych toppled Kevin Anderson of South Africa 7-5 6-2 in their third-round clash, but seventh seed Juan Martin del Potro was on the end of an upset as he fell 6-4 7-6 (7/3) to French world number 36 Benoit Paire.