The 23-year-old featured for the full 90 minutes in Saturday's win over Las Palmas, but now faces a spell on the sidelines after suffering a muscular problem.
"Rafinha has pulled a hamstring muscle and will have to sit out this Thursday's Copa del Rey first leg away to Real Sociedad," a statement on the club's official website read.
"The club doctors will need to monitor the Brazilian's progress before determining his availability for other matches.
"The injury is to the attacking midfielder's biceps femoris muscle in his right leg."
Rafinha has made 18 appearances for Barcelona in all competitions this season, netting six goals.