The Dutch striker was injured in an international friendly against Germany in Amsterdam last week, pulling a thigh muscle.
"Afellay will in all likelihood miss training and he is also unlikely to play," Schalke 04 coach Huub Stevens told reporters on Tuesday. "It would be too dangerous to play him."
Stevens said he would also likely have to make do without defenders Christoph Metzelder and Atsuto Uchida, both back from injuries but still some way from full fitness.
"Metzelder and Uchida are still building up intensity in training and it would be a risk to play them at this point," Stevens said. "We still have to decide about that."
Schalke's back-line looked out of sorts in their 2-0 defeat to Bayer Leverkusen on Saturday.
The Germans, top of Group B on eight points with Arsenal a point behind in second, will secure a last 16 place for the second time in three seasons with a win over the Greek champions.
"We have written off the Leverkusen game and the only thing we are focusing now is to get to the next round," said Stevens.
"We accept the criticism for our performance against Leverkusen but what is more important is the entire picture after 34 league matches."
Schalke are in second place in the Bundesliga, eight points behind leaders Bayern Munich.
