Abramovich’s spokesman John Mann told BBC Sport the rumours, which originated at Russian business news channel RBC, were false.
The station had promised details of the arrest in its 6pm bulletin, but failed to substantiate the rumours, which quickly spread on Twitter.
Mann did however confirm the 46-year-old is in the US. Abramovich is believed to have docked his superyacht in New York as his partner Dasha Zhukova prepares to give birth, The Telegraph reports.
Shares in London-listed steel maker Evraz, of which Abramovich is a 63 per cent owner, dropped 5pc amid the arrest rumours. They rose again as the rumour was denied.