Lewis Morgan is facing four or five weeks out of action after undergoing knee surgery on Monday.
The former St Mirren winger played for 13 minutes of the 3-0 win away to Alashkert but missed out on the games against Standard Liege and Alashkert at home.
According to a report in the Daily Mail he underwent keyhole surgery on a knee on Monday and is likely to be unavailable for a month.
Morgan looked impressive in his brief appearance in Armenia but will effectively be starting again when he recovers from injury.
After appearing interested in sending Mikey Johnston out on loan last weekend Brendan Rodgers ruled that option out when he spoke to the media on Tuesday.
Already this early in the season Celtic are starting to accumulate injuries with Jonny Hayes and Marvin Compper both currently injured.
Mikael Lustig will return to training on Monday and could feature in the away tie with Rosenborg with Tom Rogic an option for the home leg.