The court said no hearing date had been fixed yet for the athlete, who is a member of the Olympic Athletes from Russia (OAR).
The Russians were competing under a neutral flag, but Alexander's teammates were surprised when he was leaving as they insisted he could not have done anything wrong.
The IOC has reacted to the development, as spokesman Mark Adams backed the selection of athletes from Russian Federation, he however expressed his disappointment and took a stance that doping cases should be looked at from an individual point of view and not as a group.
A reported doping case involving a Russian athlete could affect whether or not his team will march behind the Russian flag at the closing ceremony of the PyeongChang Winter Olympics.
"It's stupid but Alexander is not stupid so I don't believe it", said Russian women's curling coach, Sergei Belanov. His first sample had tested positive for the substance, which was banned by the World Anti-Doping Agency in 2016.
He echoed a general bewilderment among curling athletes who couldn't fathom why anyone would use drugs that aid endurance in a sport that needs steady hands and concentration rather than peak physical fitness.
"I can't imagine what kind of drugs you could use in curling.so it's very hard to believe".
Russian athletes are banned from competing for their country at Pyeongchang due to allegations of systematic doping.
Russian Curling Federation president Dmitry Svishchev said Krushelnitsky tested clean as recently as January 22.
Moiseeva said it would be awful if the case hurt Russia's chances of regaining full Olympic status for future Games.
Russian sports officials are to meet anti-doping officers at Pyeongchang, the source said, adding that any violation would only be confirmed after analysis of a "B" sample. In total, more than 170 athletes, including over 40 Russians, have tested positive for the drug since it was banned. Meldonium is the same substance that tennis star Maria Sharapova tested positive for in 2016, leading to a 15-month suspension.