The 25-year-old attacker has been out of action since tearing the anterior cruciate ligament in his left knee in September, just days after recovering from a hamstring problem sustained in pre-season.
He had set foot on the training pitch for the first time last month and, according to EFE, was able to train with the rest of his team-mates in Sunday's practice session.
However, it is understood that it will still take some weeks before Afellay can play again due to a lack of match sharpness.
Meanwhile, Eric Abidal, who missed Saturday's 2-0 victory against Sevilla, also took part in the session as he awaits his liver transplant.
Barca will host Granada on Tuesday in their upcoming La Liga fixture.