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 was taken to hospital after his arrest.
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.
A spokesman for Ireland’s Department of Foreign Affairs and Trade told the BBC: “We are aware of an Irish citizen having been arrested in Rio. The department, through its consulate in Rio, is following up and stands ready to provide all appropriate consular assistance.”
Sports minister Shane Ross, who is in Rio and who recently met Mr Hickey, tweeted simply: “Shell shock here in Rio.”
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.
The OCI said in a statement it was “aware of the media stories regarding Pat Hickey and we are seeking total clarity on the situation before we comment further”.
Mr Hickey is president of the European Olympic Committees, the body, which gathers the continent’s 50 national Olympic committees together.
The Irishman was detained at his hotel near the Olympic park early on Wednesday morning.
According to reports in the Irish press, his wife initially told police that he had left, only for him to be found in another hotel room.
His passport and Olympic ID were seized and were later displayed to photographers at a police press conference.
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 Sports 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.
THG Sports is owned by Marcus Evans Group, which also owns Ipswich Town Football Club.
Marcus Evans was one of four names on a list of arrest warrants issued by a Brazilian judge on Monday in connection with the alleged reselling of Rio 2016 tickets.
None of those four people is thought to be in Brazil and police there have said they will pursue the matter with Interpol.
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 International Olympic Committee’s executive board since 2012.