"It's a complicated sort of tear," Argentina's national team doctor Donato Villani was quoted as saying in the Spanish media on Thursday. "He's going to need three or four more weeks treatment.
"In my opinion he will only be ready to play one more game this season and that will be the Champions League final."
Barcelona meet Milan in the first leg at the San Siro on Tuesday before hosting the return match at the Nou Camp on April 26.
Argentine international Messi, 18, has been out of action since the Champions League first knockout round second leg against Chelsea at the beginning of March.
Barcelona medical chief Lluis Til was not as pessimistic as his Argentine counterpart but made it clear Messi was unlikely to play in either of the games against Milan.
"He won't play in the first leg and it's practically impossible he'll be ready in time for the second," said Til.
The injury sustained by the exciting Messi means Sweden striker Henrik Larsson is likely to retain his place in the starting line-up against Milan.
