Chessum suffered the injury during the squad’s training camp in Girona last week and the PA news agency understands he is undergoing scans, the final results of which should be known on Sunday.
The 24-year-old is now sweating on his availability not only for the All Blacks’ visit to Allianz Stadium, but also the remainder of the campaign against Australia, South Africa and Japan.
If ruled out, the Leicester back five forward would be a significant loss to head coach Steve Borthwick.
Chessum provides options in the second and back rows and it was at blindside flanker where he made a strong finish to this year’s Six Nations with impressive displays against Ireland and France.
He would have toured Japan and New Zealand in the summer with the expectation of adding to his 23 caps, only to be sidelined by shoulder and thumb issues that needed surgery.
A recipient of one of 17 enhanced Elite Player Squad contracts announced on Friday, he could now be facing another lengthy interruption to his Test career.
Northampton scrum-half Alex Mitchell has already been ruled out of the autumn because of a neck injury and there is uncertainty over the return dates of George Ford and Fraser Dingwall.
Centre Henry Slade is aiming to prove his fitness after shoulder surgery in Exeter’s clash with Harlequins on Sunday in what will be his first appearance of the season.