RBC's initial report was quickly picked up by other news outlets, but few other details are available at present.
Business Insider reached out the to FBI who would not confirm or deny there was an investigation.
In a statement to the Independent's Shaun Walker, Abramovich's spokesman John Mann said that his client was in the US but had not been detained or arrested in any way. An official tweet from Mann says that the reports of an arrest are "NOT TRUE".
According to the Telegraph's Tom Parfitt, RBC's story was based on "rumors":
Just watched @ru_rbc 6pm Moscow bulletin. Smoking gun on Abramovich "arrest" turned out to be "rumours" which it cannot substantiate.
— Tom Parfitt (@parfitt_tom) March 25, 2013
Abramovich, the billionaire business tycoon who owns London's Chelsea Football Club, has been in the news in the past few days after the sudden death of a rival UK-based oligarch, Boris Berezovsky.
Abramovich had recently beat Berezovsky, once his business partner and mentor, in one of the costliest legal cases in UK history. Berezovsky's death is not being treated as suspicious at this time.
Shares of Russian steelmaker Evraz tanked the arrest report. Abramovich is a major shareholder in the company.