He and mixed doubles curling partner Anastasia Bryzgalova beat a Norwegian pair to win bronze at the games in South Korea.
Calls for an outright ban at the Pyeongchang Games grew louder in recent months after the International Olympic Committee stripped several Russian medals and banned dozens of athletes from the Games for life for doping at the Sochi 2014 Winter Olympics.
The athlete, who won the medal with his wife, had accepted a provisional suspension beyond the period of the Games.
Twitter has been filled with mentions that "Shattered" and not the Olympic theme song should have played when the Olympic Athletes from Russian Federation entered the Olympic Stadium for the opening ceremony.
The Russians, who are competing at the Pyeongchang Games as neutral athletes and under the Olympic flag because of a vast doping scheme at the 2014 Sochi Games, said Tuesday they want to open a criminal investigation to find out who could have caused this positive result.
He was stripped of his Pyeongchang Winter Olympics bronze medal Thursday.
The athlete has said that the positive tests were a shock, while Russia's sports minister Pavel Kolobkov said that there was no point for him in taking the endurance-boosting drug as it was "pointless" for curling.
In a statement, the delegation said the second set of results indicated Alexander Krushelnitsky only consumed meldonium once.
Russia's chances of waving the national flag at the closing ceremony appeared to diminish after Olympic curling bronze medalist Alexander Krushelnitsky tested positive for the banned substance meldonium.
In a statement posted to Twitter Sunday, the International Olympic Committee declined to comment on individual cases, but said it took note of the statement by the OAR spokesman.
"I hope this will not influence the decision of the International Olympic Committee (IOC) on February 24 on the return of Russian Federation into the Olympic family". Athletes who passed a rigorous screening process were allowed to compete as "Olympic Athletes from Russian Federation".
Krushelnitsky and Bryzgalova became the first Russians to participate in the Pyeongchang Games when they competed in a preliminary-round game on February 8, the day before the opening ceremony.
The statement said it would be "useless and senseless" for Krushelnitsky and Bryzgalova to fight the doping case during the Olympics but added that they considered themselves "clean athletes".
The OAR said Krushelnitsky provided a clear drug sample on January 22 and that for Meldonium, which increases blood flow, to be performance-enhancing it must be used regularly and over a prolonged period.