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.
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
