The Spain international picked up the injury in Saturday's 3-1 La Liga defeat at Real Sociedad, which allowed Real Madrid, 3-0 winners at home to Elche, to pull three points clear at the top.
Barca are already without left back Jordi Alba, another Spain international, who missed the Sociedad game with a thigh muscle strain.
Pique is likely to sit out La Liga games at home to Almeria and away at Real Valladolid but should be fit for Barca's Champions League last 16, second leg against ManchesterCity on March 12. Barca won last Tuesday's first leg in Manchester 2-0.