Vasily Aleksanyan was detained in a raid by armed police on March 7.
Aleksanyan, who denies any wrongdoing, asked the court to release him pending further investigation.
Prosecutors argued there was a risk Aleksanyan would try to leave the country or destroy evidence relating to the case.
Yukos issued a statement protesting Aleksanyan's arrest, saying the police raid, which was shown on national television, showed Yukos could be attacked with "essentially no repercussions."
Yukos, once Russia's biggest oil producer, was crippled by billions of dollars in back taxes and its founder, Mikhail Khodorkovsky, imprisoned on fraud and tax evasion charges after a trial widely seen as punishment for his political ambitions.