"It is a partial tear of the Achilles tendon which means he will be unavailable for around six months," said a Perpignan spokesman.
"It's a huge disappointment, especially for him and for the club."
Carter only joined the French outfit in December and has played just five games for his new side but he is now unlikely to play for them again before moving back to New Zealand.
Having been offered a sabbatical by the New Zealand Rugby Union, Carter is due to return to his home country in June, by which time he still may not be fully recovered from his injury.
"Now we are going to do our best possible to get him healthy again," explained the Perpignan spokesman.
"Our doctor will be in contact with the medical staff of the All Blacks to decide whether or not he will undergo surgery in France.
"At the monent he is in plaster and is at home. He underwent an examination on Sunday morning and returned with us by plane."