The 37-year-old defender, who moved to the Ricoh Arena from Wigan this summer, damaged medial ligaments in a knee during training.
"I feel for Arjan because I know how much he was looking forward to the start of the season," manager Iain Dowie said.
"It was a freak accident and we are pleased that it isn't more serious than it is, he has been a model professional since he joined the club."