Mr Hickey, 71, is suspected of illegally passing on tickets for the Games to be sold on at extortionate prices, Brazilian media report.
Mr Hickey, said to be unwell after his arrest, has not yet commented publicly.
Police say the suspect, who also heads the Olympic Council of Ireland (OCI), tried to escape when they came for him.
They say he slid his Olympic pass under the door when police came knocking and fled into the adjacent hotel room, where his son had been staying until recently.
After he was arrested he was taken ill and received medical attention, reports say.
Brazilian media believe Mr Hickey's arrest is related to that of fellow Irishman Kevin James Mallon on the day of the Olympic opening ceremony.
Mr Mallon is the director of THG Sports, a sports hospitality company alleged to have resold tickets for Rio 2016 illegally.
When Mr Mallon was arrested on 5 August, he was found to be in possession of more than 800 top-class tickets for the Games.
Police suspect they were to be sold at prices of up to £6,000 ($7,800) each.
THG said Mr Mallon had not sold or sought to sell tickets but had been holding them for collection by clients of the Irish authorised ticket reseller, Pro 10 Management.
The OCI said it would launch an inquiry into the ticket sale controversy but has been criticised for rejecting a call by the Irish Sports Minister to bring in independent investigators.
Last week, the OCI wrote on its website there was “absolutely no suggestion of misconduct or impropriety” by the OCI or any of its staff.
Mr Hickey was elected head of the European Olympic Committees in 2006 and has been in charge of the Olympic Council of Ireland since 1989.
He has also been on the IOC executive board since 2012. (BBC)
•Photo shows European Olympic Committee Head Patrick Hickey.
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