"The unfounded and absurd decision once again demonstrates the IOC's inability to eschew external influences on its decision-making," the federation said in a statement.
The federation is poised to "immediately start fighting to restore a fair attitude towards Russian figure skaters and defend the honour and dignity of our athletes in all possible ways".
Stolbova and partner Fedor Klimov, who won silver in the pairs and gold in the team event in Sochi, took silver at the European championships in Moscow last week.
Stolbova could not immediately be reached for comment.
Bukin, who competes in ice dance with partner Alexandra Stepanova, won a European bronze medal this month.
The news came hours after the Russian Olympic Committee announced that short-track speed skater Viktor Ahn, biathlete Anton Shipulin and cross-country skier Sergei Ustyugov were not in the pool of Russian athletes eligible to compete at the Pyeongchang Olympics.
Five members of the Russian men's national hockey team, Anton Belov, Alexei Bereglazov, Mikhail Naumenkov, Valery Nichushkin and Sergei Plotnikov, were also deemed ineligible for Pyeongchang by the IOC, the Russian hockey federation said in a statement later on Tuesday.
Belov, a defenceman who played one season with the Edmonton Oilers of the National Hockey League (NHL), served a three-month doping suspension in 2012.
The Russian hockey federation said it would seek explanations from the IOC about the players' exclusion.
The Olympic body said on Tuesday that the exclusion of certain athletes from the list of eligible Russians did not mean they had doped.
"Not being included on the invitation list does not necessarily mean that an athlete has been doped – it should not automatically cast doubt on their integrity," Valerie Fourneyron, chair of the panel overseeing the invitation process, said in an IOC statement.
The IOC banned Russia last month from Pyeongchang over "systematic manipulation" of the anti-doping system at the 2014 Sochi Games, but left the door open to athletes with no history of doping to compete as "Olympic Athletes from Russia".
(Writing by Polina Ivanova and Gabrielle Tétrault-Farber, additional reporting by Karolos Grohmann in Berlin; Editing by Ed Osmond and Christian Radnedge)
