"We didn't arrest him. It's just not true," an FBI spokeswoman said in response to an unsourced report by Russia's RBK financial news portal that Abramovich had been held in the United States.
The RBK report followed media speculation over the unexplained death of exiled Russian tycoon Boris Berezovsky at his home near Ascot, the man who launched and lost a multi-billion-dollar court case last year against Abramovich, his former business partner.
Abramovich's Moscow spokesman, John Mann, said earlier that the report was false.
"He is in the US but he has not been arrested or detained," Mann said.
As well as owning Chelsea, the 46-year-old Abramovich is a major shareholder in London-listed steel firm Evraz, whose shares fell by more than 6 percent before recovering to trade 3.4 percent down on the day.
The London-based tycoon is reputed to have close ties to the Kremlin. Forbes magazine estimates his fortune at $10.2 billion (£6.7bn).