The champions confirmed on Friday that Arthur has begun treatment on the problem, which could reportedly keep him sidelined for up to three weeks.
The news is a blow to Barca coach Quique Setien, who is already without Luis Suarez, Ousmane Dembele and Sergi Roberto for the visit of Sociedad.
Youngsters Riqui Puig and Alex Collado have been called up to the 18-man squad for the meeting at Camp Nou.
Arthur could now be a doubt for Barca's Champions League last-16 clash with Napoli on March 18, with the first leg in Italy having finished 1-1.
The 23-year-old was included in Tite's Brazil squad for their World Cup qualifying matches against Bolivia and Peru this month, despite his injury.