The International Bobsleigh and Skeleton Federation (IBSF) had come under pressure to move the event from the host city.
The International Bobsleigh and Skeleton Federation (IBSF) had come under pressure to move the event from the 2014 Winter Olympics host city after last week's damning report by Canadian law professor Richard McLaren which implicated more than 1,000 Russian athletes in at least 30 sports in a state-sponsored doping programme.
"The IBSF executive committee felt that during this difficult time it is prudent not to organise such an event in Russia," a statement by the sports governing body read, adding a new location would be decided in the coming days.
Kremlin spokesman Dmitri Peskov reacted immediately, saying Russia "enormously regretted" the decision.
"We're convinced that this was a political decision. It's based on statements without any evidence," Peskov was quoted as saying by the R-Sport agency.
Russian Sports Minister Pavel Kolobkov expressed his surprise. "There is an agreement for the organisation of these world championships that no one has terminated," Kolobkov told R-Sport.
"We must look very carefully at the agreement signed by our Federation with the International Federation. We will clarify these issues and make decisions in the future."
The announcement comes four days after the final publication of the McLaren report in which the Canadian lawyer described how Russia "hijacked" sport by involving more than 1,000 athletes in an "institutional conspiracy" to win by mass doping at the Sochi 2014 Winter and London 2012 Olympics and other global competitions.
McLaren, who detailed in a previous report how Russian security services were involved in the nefarious scheme, said in a second report for the World Anti-Doping Agency (WADA) that at least 30 sports were implicated and that salt and instant coffee were used to manipulate Russian samples.
"This decision was made for two primary reasons," the IBSF said of its ruling on Tuesday.
"First: 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.
"Second: The Russian Bobsleigh Federation has put a great effort in the preparation of the World Championships, but the current climate would make it nearly impossible to appreciate the efforts of the organising committee to host a great event or the quality of the Sanki Sliding Center as one of the best tracks in the world.
"Having stated that, 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."
Latvia's powerful skeleton team had announced they would be boycotting the event in the Black Sea venue, saying on Sunday its giant neighbour had "stolen" the Olympic spirit.
Latvia finished second in the medals table in skeleton at the 2016 world championships.
USA Bobsled & Skeleton chief Darrin Steele had told AFP that most US athletes due to take part in Sochi from February 17-26 had voiced concerns about competing in Russia.
The British Olympic Committee had also said they were ready to "support" a boycott.
The International Olympic Committee (IOC) responded to McLaren's damning report by announcing it would reanalyse all 254 urine samples taken from Russian athletes at the Sochi Winter Olympics.
Russia's track and field team were already banned from international competition for doping and barred from the Rio Olympics in August, but there is now growing pressure for more sanctions.