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Schmeichel suffered the injury during the first half in his native Denmark but got through the game and made a couple of late saves as Leicester edged closer to the last 16 of Europe's elite club competition.
The 29-year-old, a key figure for Leicester in their run to being crowned champions of England last season, was due to see a specialist on Thursday and could be out for as long as six weeks depending on medical advice.
The 29-year-old is set to see a specialist to determine the extent of the injury following Leicester's return to England later on Thursday.
"Leicester City goalkeeper Kasper Schmeichel is set for a spell on the sidelines after fracturing his hand in Wednesday's UEFA Champions League draw in Copenhagen," said a club statement issued Thursday.
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"The Denmark international injured his right hand during the first half of the goalless draw at Parken Stadium and will see a specialist upon returning to the UK with the rest of the squad on Thursday."
Schmeichel, at the very least, is now set to miss the Premier League matches against West Bromwich Albion, Watford and Middlesbrough, as well as the Champions League game at home to Brugge.
Ron-Robert Zieler will deputise for Schmeichel, starting with Sunday's match at home to West Brom.
The German keeper, a pre-season signing, has already gained Premier League experience this term during matches Swansea, Burnley and Manchester United, as well as the EFL Cup tie against Chelsea.