Mr Hickey, 71, is suspected of illegally passing on tickets for the Games to be sold on at extortionate prices, the reports say.
His arrest comes days after a man was caught in Rio with 800 illegal tickets.
Police say Mr Hickey, 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 opening ceremony.
Mr Mallon is the director of THG Sports, a sports hospitality company alleged to have resold tickets for Rio 2016 illegally.
When he 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 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.
European Olympic Committees head `arrested in Rio` - Patrick Hickey
17 August 2016
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The head of the European Olympic Committees, Patrick Hickey, has been arrested in Rio over illegal Olympic ticket sales, Brazilian media report.
