The match, played in front a tiny crowd in Brasilia, preceded the day's other Group A clash between hosts Brazil and South Africa.
Both Iraq and Denmark were unperturbed by the 80 degree temperatures and set out to play open and attacking football at the 72,000 capacity National stadium.
Denmark hit the post after three minutes but Iraq had the best chances, with Ali Adnan forcing the Danish keeper into three good saves from free kicks.
The first goals in the competition came later on Thursday in Rio, where Honduras beat Algeria 3-2 in an enthralling match.
Honduras player Antony Lozano (L) vies for the ball with Algeria player Demmou Abdelghani during the Rio 2016 Olympic Games men's First Round Group D football match Honduras vs Argelia, at the Olympic Stadium in Rio de Janeiro on August 4, 2016.
Image credit: AFP
Romell Quioto got the opener after 13 minutes and Marcelo Pereira added a second 20 minutes later.
Sofiane Bendebka got one back for Algeria midway through the second half only for Antony Lozano to restore Honduras' two-goal advantage after 79 minutes.
Baghdad Bounedjah got a second for the Africans with five minutes remaining and, although they pushed hard for an equaliser, Honduras took all three points.
Brazil were held to a 0-0 draw by South Africa in their Olympic Games opener at Estadio Nacional Mané Garrincha in Brasilia.