The court said no hearing date had been fixed yet and no further information would be provided for the moment.
Krushelnitsky, who competes in curling, is suspected of testing positive for meldonium, a banned substance that increases blood flow and improves exercise capacity.
Krushelnitsky, who won bronze with his wife in mixed-doubles curling in Pyeongchang, has not responded to a request for comment.
Russia's curling federation has also launched an "emergency commission" to investigate the doping case, federation president Dmitry Svishchev told Reuters.