Olympic team pursuit gold medallist Burke suffered the injury after crashing during team time trial training on the Spanish island of Majorca on Sunday, British Cycling reports.
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Burke, 26, said: “I’m really disappointed to be injured at this stage of the season, but I’ve been in the gym today and hope to be back training on the turbo this week.
“I aim to be back on the track as soon as possible so that I can resume training for the track world championships at the end of February.”
Great Britain technical director Shane Sutton added: “The accident on Sunday was unfortunate, particularly as Steve had been showing some great form of late, but these things do happen and we have an excellent team of people who will help Steve get back to full fitness as soon as possible.”
Burke, 26, was one of eight riders named in the new British-based UCI Continental outfit Team Wiggins. The squad is due to field a team in the forthcoming Challenge Majorca races at the end of January.
Burke continues to be a mainstay of Great Britain’s team pursuit line-up, which won during London round of the Track World Cup in December.