The Brazilian pulled up shortly before half-time during Barca's 3-1 La Liga win at home to Celta Vigo and had to be replaced by compatriot Daniel Alves.
Adriano, who scored Barca's opening goal at the Nou Camp, joins centre-backs Carles Puyol and Gerard Pique on the sidelines and will be unavailable for Wednesday's Champions League match at Celtic.
"Adriano suffered a strain to the adductor muscle in his right leg and will be out for approximately three weeks," Barca said in a statement on their website.
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