The business is marking Iceland's achievement of becoming the smallest nation ever to qualify for the tournament.
The "Icelandair Team Iceland stopover" activation will be available for all passengers between May and June, and include activities around culture, fitness and well-being.
There is a chance to "learn how to cheer like some of the most passionate fans in the world" by attending a national men’s or women’s team match. Midfielder Birkir Bjarnason is inviting fans to Laugarvatn Fontana where they can "unwind like a pro" in the geothermal baths.
Dagný Brynjarsdóttir has set up a training session with a backdrop of the views of the country; younger passengers could be in with a chance of a 90-minute session at the Breidablik Academy; and player Gylfi Sigurðsson has picked out one of his favourite golf courses in Iceland where passengers can spend time with him to perfect their swing.
The campaign has been created by The Brooklyn Brothers and Íslenska.
Björgólfur Jóhannsson, president and chief executive at Icelandair, said: "We are continually looking at ways to enhance our customer experience and hope that passengers will enjoy time well-travelled this summer through this value-added offering.
"Not only can our passengers find out more about the backstory of this legendary team, but we’ve worked with the players to personally design these experiences, allowing our passengers to follow in their footsteps."