The versatile Brazilian full-back had to be substituted in the first half of Barca's home league match against Rayo Vallecano after stretching to control a ball.
Adriano is set to miss the Champions League quarter-final against Paris Saint-Germain which takes place in the first two weeks of April.
The injury-prone Adriano will be sidelined along with captain Carles Puyol, who had knee surgery last week, leaving Barca short of options in defence going into the critical phase of the season.
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