The British number one and world number four will face Gilles Simon in the last 16 after the Frenchman beat Austria's Juergen Melzer.
Canada's world number 26 Raonic picked up the ankle injury in practice and was forced to withdraw three games into a doubles match on Saturday.
He had hoped to play with a night's rest but decided to withdraw in the build-up to the match.
Simon had to weather a back problem in his 7-6(5) 6-4 win, the number 13 seed taking an injury time-out during the first-set tie-break.
Simon has 48 hours to get his back close to 100 per cent and prevent the prospect of a second bye for the Scot.
Murray beat Colombia's Alejandro Falla in the second round.