Balotelli sustained the injury during a training session on Tuesday and sat out Thursday's Europa League 2-0 defeat at Schalke 04 that sent the Azurean side out of the competition.
"He will not be there for the next three games in the 10 coming days," Favre was quoted as saying on the club's website (www.ogcnice.com).
"For the games that will follow, we don't know yet."
Balotelli will therefore miss Sunday's home game against Bastia, the trip to En Avant Guingamp and another home match against Toulouse.
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There was more bad news for Nice with Favre confirming that defender Paul Baysse, who has been out for more than a month after starting the first nine league games, will not play until the end of the year because of a knee problem.
Nice have 32 points from 13 games and lead second-placed Monaco and third-placed Paris St Germain by three points.
(Reporting by Julien Pretot; Editing by Nick Mulvenney)
