The triple grand slam winner, who will take over from Serb Novak Djokovic at the top when the rankings are updated on Monday, still went out on centre court for a practice session in front of a bemused crowd.
“I never thought I’d be No. 1 in the world and never, never imagined that was something that was going to happen,” Murray told a news conference.
Fourth seeded Canadian Raonic explained his injury.
“Yesterday at I believe 4-2 in the first set I started feeling some pain in my leg,” he said, referring to his match against Frenchman Jo-Wilfried Tsonga.
“I didn’t think too much of it at that point. I had an MRI half an hour ago…they found that I have a grade one tear in the right quadriceps.”
Raonic is now doubtful for the season-ending ATP World Tour Finals to be held in London from Nov. 13-20.
“I still have the possibility of making it but I was told five to 10 days so I’m on the borderline,” he said.
Murray is the first Briton to get to number one and, at 29 years and 174 days, he will be the oldest player to reach the summit for the first time since Australian John Newcombe in 1974.
Djokovic, number one for 122 weeks since July 2014, was knocked out in the quarter-finals by ninth seed Marin Cilic on Friday.
Croat Cilic lost 6-4 6-3 to American John Isner in the semi-finals on Saturday.
Isner broke in the ninth game of the first set and served three aces in a row as he saved a break point in the second to down Cilic, who appeared to lack focus a day after eliminating Djokovic.
Isner became the player to serve the most aces this year – 1,133 – as he claimed his first victory over Cilic in seven matches.
“I took the court today with a lot of confidence. It’s the first time all year coming into a match I’d won four matches in a row,” Isner told a news conference.
“So I knew I was playing well. I knew I was playing the right way, and really, from the get-go, I was serving extremely well. That took a lot of pressure off me.
“I was just taking my cuts from the back of the court. Returning pretty well, returning aggressively. I certainly put it all together today. It was the best match I have played all year.”
(Editing by Ed Osmond)