The seventh-seeded Raonic was scheduled to play U.S. Open finalist Kei Nishikori of Japan, but was replaced in the Group B pool by Spanish substitute David Ferrer.
Raonic, who was 0-2 at the year-end event, said he suffered the injury late in the first set of Tuesday's 6-3, 7-6 loss to Murray.
"At first it felt like cramping but when I got up from a changeover and had to stand, I knew it was something else," he said.
The 23-year-old Canadian said the low-grade tear in his quadriceps muscle measures three by five centimetres and is about a centimetre deep.
"Obviously I feel pessimistic right now," Raonic said, adding doctors told him playing might risk more damage and cost him up to six weeks of recovery time. "I had a great time here. It was very different from last year as an alternate.
"Fortunately I was able to play well in my last event (Paris) to qualify here and give myself opportunities. I wish I could have competed, but it is what it is."
Six-time champion Roger Federer will take on Andy Murray in the other Group B match. If the 17-time Grand Slam champion beats Murray and Nishikori defeats Ferrer, then the Scot will be eliminated from the indoor event.
Also Thursday, Toronto's Daniel Nestor and Serbian partner Nenad Zimonjic signed off on their doubles partnership with a 6-7 (5), 6-3, 11-9 win over Spaniards Marcel Granollers and Marc Lopez. Nestor and Zimonjic improved to 1-2 but did not qualify for a spot in the weekend semifinals.
Ferrer, who trained in London this week, has no chance of making it to the singles semifinals.
At the Paris Masters last month, he saw his hopes of qualifying for the Finals vanish after losing a tough battle to Nishikori in the quarter-finals. The Spaniard came within two points of victory but failed to hold on to his lead.
Raonic, from Thornhill, Ont., said he was looking forward to facing Nishikori, who had won four of their five meetings.
"This experience this week motivates me a lot," he said. "I felt I did pretty well, but know I can do a lot better. My season has been consistent, but I would have liked to have had a few more chances to win big matches.
"I really badly wanted to play, the competition here is about facing the best and being on top of your game."
The eighth-ranked Raonic said it came down to weighing the merits of playing at half-speed and risking further injury or ending his season with prudence.
"It would be unfair to fans if I were to step out there and play a mediocre match all way through or if things got worse and I had to stop," Raonic said. "The doctors said that if I were to play I'd be walking a tightrope.
"That was a factor in my decision, I didn't want to accept it, but I had to listen to the doctors and my team."
Raonic, one of the three newcomers in London with Marin Cilic and Nishikori, picked up his sixth career singles title with a victory at The Citi Open in Washington last August. A month earlier, he reached a career-high No. 6 in the world rankings.
Raonic made his first French Open quarter-final appearance this year and also advanced to the semifinals at Wimbledon for the first time.
Nestor and Zimonjic, two-time champions at this event, will team up with different players next season. The 42-year-old Nestor is tabbed to play with India's Rohan Bopanna.
The Nestor-Zimonjic duo closed out their second run as partners with a flourish, mounting a comeback in the match tiebreak by winning six straight points. They saved a match point before Zimonjic came through with two straight volley winners for the victory.
They entered the match with a slim chance of reaching the semifinal round and were officially eliminated from contention when they dropped the first set.
"Any time you win a match, it's more good than bad," said Nestor. "We had our chances in the opening set, that will make today a bit tougher to remember. But in the last match of the season we played well, that's all you can ask.
"There were still ranking points at stake. I thought I was playing well and Ziggy was playing well also."
With files from The Associated Press.Suggest a correction