The tie will take place over one leg because of the competition’s revised schedule due to the impact of the coronavirus pandemic.
Celtic Park will likely host the game on August 18 or 19, but there is still a possibility the fixture could be staged at a neutral venue.
Neil Lennon’s Scottish champions face up to four qualifying rounds in total.
The Hoops’ only previous meeting with KR Reykjavik came in a Champions League qualifying tie in the 2014-15 season when they progressed 5-0 on aggregate.
Irish champions Dundalk have been drawn against Slovenian side Celje, while Cymru Premier winners Connah’s Quay take on Sarajevo.
Northern Irish side Linfield face Drita of Kosovo in the final of the preliminary round in Nyon on Tuesday, and the winners of that tie will earn a clash against Legia Warsaw.
UEFA will conduct the draw for the second qualifying round on Monday, with those matches scheduled to be played on August 25 or 26.
In the Europa League preliminary round, Northern Irish pair Glentoran and Coleraine will take on HB of the Faroe Islands and La Fiorita from San Marino respectively.
Barry Town United, meanwhile, face Faroese outfit NSI Runavik, with matches due to take place on August 20.