Brazilian police claim he was involved in a scheme to resell Olympic tickets at higher than their face value.
They said the scheme could have had profits of 10m reals (£2.4m; $3.1m).
Mr Hickey will be replaced as president of the European Olympic Committees - the body which brings together the 50 national committees across the continent - by his deputy Janez Kocijancic.
The Olympic Council of Ireland (OCI) said in a statement that Mr Hickey was stepping aside "until this matter is fully resolved" and would continue to co-operate and assist with all enquiries.
Acting OCI President William O'Brien said the council would "defend ourselves to the hilt" after the arrest of Mr Hickey.
Mr Hickey, a former judoka, has been a member of the 15-strong executive board of the International Olympic Committee since 2012, making him a prime mover in the world of international sports.