The Hoops skipper lasted less than a minute of yesterday's 1-1 friendly draw against Rapid Vienna in Austria before pulling up with a hamstring injury.
He is expected to be sent for scans today to determine the full extent of the damage to his muscle.
Brown was carried off on a stretcher clearly in a lot of discomfort, and, if there has been a tear, could be out for between three and six weeks.
A Hoops spokesman said: "The captain is still being assessed by the club's medical staff and the extent of the injury is not yet known."
Ronny Deila's side travel to Iceland a week today for their first-leg tie the following night.
The return is seven days later at Murrayfield, and defeat for the Hoops over the two legs would see them crash out of Europe for the season as there is no parachute into the Europa League at this stage of qualification.
That would give Deila the same start to his reign as manager as was suffered by Gordon Strachan when, in 2005, his first match in charge was the 5-0 defeat to Artmedia Bratislava.
Although the Hoops won the return leg 4-0, they had to wait another 12 months before they could return to the European stage, when, of course, they reached the last 16 of the Champions League for the first time in the club's history.
Deila's limited experience of competing in European competition means he will lean heavily on the likes of Brown, who has been over the course many times before.
So, it would be a major blow if the skipper was ruled out of these ties.
And, with the third qualifying round ties scheduled for July 29/30 and August 5/6, Brown would be facing a race against time to recover for them, also, if the diagnosis on his injury confirms it is at the serious end of the scale.
Deila could also be dealt a setback if he tries to bring Georgios Samaras back to the club.
The Greek striker has reached the end of his contract at the club, and insisted he had not been offered a new deal. Deila has admitted that he is considering re-visiting that situation.
But, after a decent World Cup in Brazil with Greece, Celtic would face serious competition for Samaras' signature.
Lazio are the latest club credited with an interest in acquiring his enigmatic skills.
Celtic have also been linked with 18-year-old Iraqi attacking midfielder, Hammam Tariq, who is currently with United Arab Emirates side, Al Ahli.