The French international went off in the 26th minute of Wednesday's 3-0 Champions League last-16 second leg victory over Borussia Dortmund, a win that took Juve through 5-1 on aggregate.
Pogba's injury could mean he misses the quarter-finals and, if the team qualify, the semi-finals too.
Coach Massimiliano Allegri may decide to switch to a three-man defence in Pogba's absence with Claudio Marchisio, Arturo Vidal and Andrea Pirlo patrolling the midfield.
Juventus, who have a 14-point lead with 11 games to play as they seek a fourth straight Serie A title, host seventh-placed Genoa on Sunday.
(Reporting by Jacopo Lo Monaco, editing by Tony Jimenez)
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