Chivu picked up a knee injury during the 3-2 win at Reggina, when he did a brave diving tackle to prevent a goal.
“We played with Chivu and (Ivan) Cordoba in central defence for the third time to improve our organisation in that area, but unfortunately we lost Cristian and will have to start work on another pair of centre-backs,” said manager Jose Mourinho.
“It’s the third time since the start of the season that he has been injured. It’s a real shame.”