The 30-year-old sustained a knee injury in the 2-0 victory over Everton on Sunday.
Coyle said: “Zat suffered ligament damage. It’s not as severe as we first thought but certainly bad enough to keep him out for a period of time. There’s severe swelling in the area so I think we’ll know better in seven to 10 days when that goes down.
“But I think it’s fair to say he’ll be four to six weeks, which is a terrible loss, first and foremost for Zat, because he’s played every game for me since I came to the football club over a year ago.
“He’s been outstanding as a player and as a man and the sooner we get him back the better. It is a blow, there’s no doubt about it, and we wish him a speedy recovery.”
