Latvia had already pulled out of the Feb. 13-26 worlds following last week's publication of the second part of the McLaren Report into Russian doping which revealed an institutional conspiracy to conceal positive tests.
South Korea, hosts of the 2018 Winter Olympics, and skeleton athletes from the United States had also been considering withdrawing from the championships in protest at Russian doping.
The new venue for the event will be decided in the next few days, the International Bobsleigh and Skeleton Federation (IBSF) said in a statement.
Germany had already said it was willing to host the competition if it was switched.
The decision to move the championships was politicised and without grounds, Russia's RIA news agency cited Kremlin spokesman Dmitry Peskov as saying on Tuesday.
Vitaly Smirnov, head of Russia’s anti-doping commission, told the R-Sport news agency that other sports could now choose to move competitions away from Russia.
"It's probably a consequence of the McLaren Report ... in principle there could be decisions on a whole range of sports," Smirnov said.
Russia is also scheduled to host soccer's 2018 World Cup finals.
TWO REASONS
The IBSF said the switch from Sochi, host city of the 2014 Winter Olympics, was made for two main reasons.
Firstly, to allow athletes and coaches from all nations to participate in a competition that focuses on sport rather than accusations and discussions, whether justified or not.
Secondly, because the organisers have worked hard to prepare for the event but their efforts will inevitably be overshadowed by recent developments.
The statement added: "The IBSF asks all members and athletes for fair play and respect which also includes the assumption of innocence for any athlete, regardless of national affiliation, until proven guilty."
Germany had ruled out boycotting the event but wanted it moved from Sochi, their bobsleigh federation (BSV) sports director Thomas Schwab told Reuters earlier on Tuesday.
"We would be very unhappy if it took place there. We have offered the International Bobsleigh and Skeleton Federation to jump in and host the event. We would welcome a move of the event to another location," he said before the IBSF announcement.
The IBSF decided to switch the championships from Sochi after saying last week it would "act promptly and decisively following the publication of the final McLaren Report" after reading and digesting it.
McLaren's report said analysis of samples from four Russians who won gold medals in Sochi had shown salt readings that were physiologically impossible.
There was also evidence of tampering with the samples of 12 Russian medallists at those Games.
(Writing by Ken Ferris and Ed Osmond; Editing by Tony Jimenez)
