Boerrigter limped out of the action during the 2-1 victory over Ross County after sustaining an ankle injury, and he has failed to recover in time for the trip to Sweden.
Talisman Georgios Samaras (toe) defender Kelvin Wilson (shin splints) were both absent from the first league match of the campaign.
But the duo travelled with the squad and should be fit to start the match as Celtic go into the tie looking to consolidate a 1-0 advantage from the first-leg.
Joe Ledley, Charlie Mulgrew and Adam Matthews all came through Saturday's game unscathed following recent injuries, and are available for selection.
Defenders Virgil van Dijk and Steven Mouyokolo will be among the substitutes along with fellow new recruit, forward Amido Balde.
On loan Celtic striker Mo Bangura is a major doubt to face his parent club for the second time in a week.
Bangura has a hamstring problem and missed training on Monday, but he has not been completely ruled out by Elfsborg boss Jorgen Lennartsson.