The Brazilian full-back picked up the injury during extra-time in Barca's 1-0 King's Cup final defeat to Real Madrid in Valencia on Wednesday.
Adriano's absence adds to coach Pep Guardiola's problems with Eric Abidal and Bojan Krkic already out of action, and captain Carles Puyol struggling with a muscle strain.
Barca have an eight-point lead at the top of La Liga with six matches left to play and meet Real Madrid again in the Champions League semi-finals which start next week.
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