Wilshere was already struggling with a knee injury and is now sick as well so will not be available to face the Belgians at the Emirates Stadium.
The 22-year-old has not played since the Gunners beat Anderlecht 2-1 in the reverse fixture in Belgium a fortnight ago, but Arsene Wenger expects him to recover in time for the Premier League match at Swansea on Sunday.
Wenger has not decided whether to start England winger Theo Walcott, who made his first appearance since January 4 following a cruciate ligament injury against Burnley on Saturday.
Arsenal could seal qualification to the knockout stages with two games to spare if they beat Anderlecht and Borussia Dortmund also overcome Galatasaray.
“If we can seal qualification I would describe the feeling as satisfied to have the job done,” Wenger said.
“We respect Anderlecht because they gave us a tough game and we had a bit of a miraculous win because we needed to go until the last minute but that was as well our quality in the game.
“We have been warned and now we want to win the game again at the Emirates.”
Since beating Anderlecht, Arsenal have recorded consecutive Premier League wins over Sunderland and Burnley, scoring five goals and conceding none.
Alexis Sanchez starred in both victories, bagging twice in each game, and Wenger believes the Chilean is starting to show his best form for the club.
“I believe he had a difficult start to integrate with the team – it was not easy for him to adapt to us and us to him,” Wenger said.
“Now he is showing how good he is. I believe what you want from every top player is not just individual quality but also a fighter.
“He shows that in every game – the header he scored (against Burnley) is a fantastic goal, not just because of the quality of the goal but because of the desire and determination as well.”