Jordan, who has a record 56 tries for the All Blacks, suffered the injury in the 43-21 win over Scotland at Murrayfield last weekend.
All Blacks assistant coach Neil Barnes said they were "hopeful" Jordan could feature when they face England on November 21 and then in the finals weekend at Twickenham from November 27-29.
Barnes told a press conference on Tuesday it was a minor tear, and that Jordan's progress would be monitored through the week but he was not going to be considered for Saturday's clash against Wales in Cardiff.
Barrett failed his initial head injury assessment following a heavy head-to-shoulder collision at Murrayfield but has since passed his next two concussion tests.
He is also not expected to feature against Wales, where the All Blacks are set to make many changes but he should return for the clash against England.
