Murray said the injury wouldn't require surgery but that he feared it might get worse if he carried on playing. His main concern was not disrupting his preparation for the Australian Open in January, the first Grand Slam of the new season.
"The Australian Open is six, seven weeks away," Murray said. "I could mess up my preparation for that.
"That off-season is so important for me, and has been for the last few years of getting myself in shape."
Murray will be replaced in the round-robin tournament by reserve player Janko Tipsarevic, who will play Tomas Berdych. Tipsarevic will start with a 0-0 record.
Murray's withdrawal will keep concerns over the busy men's calendar in the spotlight.
He is not the only player to have arrived in London hurt. Rafael Nadal said after his loss to Roger Federer he had a shoulder problem, Mardy Fish is nursing a hamstring injury, while Novak Djokovic also has an injured shoulder, putting a dampener on an event billed as the "final showdown" between the year's top eight players.
- AP