The Hungarian international midfielder aggravated an ongoing groin injury in the Baggies 2-0 defeat at Blackburn last weekend and is not travelling to play for his country in their two World Cup qualifying fixtures this coming week.
"Zoltan has a long-standing groin problem which has been getting progressively worse," Albion manager Bryan Robson told the clubs official website.
"He's seen a specialist, had a scan and he is going back to the specialist to have treatment.
"It is hard to see him being fit for the Arsenal game at this stage."