Chessum suffered the injury during the team’s training camp in Girona last week and the PA news agency understands he is undergoing tests, 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 for the rest of the campaign against Australia, South Africa and Japan.
If he is ruled out, Leicester’s back five forwards will be a significant loss for head coach Steve Borthwick.
Chessum provides options in the second and back rows and 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 tour Japan and New Zealand in the summer hoping to add to his 23 caps, only to be sidelined by shoulder and thumb problems that required surgery.
The recipient of one of 17 enhanced Elite Player Squad contracts announced on Friday, he could now face another lengthy hiatus to his Test career.
Northampton scrum-half Alex Mitchell has already been ruled out of the autumn with a neck injury and there is uncertainty over the return dates of George Ford and Fraser Dingwall.
Center Henry Slade is looking to prove his fitness following shoulder surgery in Exeter’s clash with Harlequins on Sunday, which will be his first appearance of the season.
Leicester director of rugby Michael Cheika revealed that Chesham is facing the sack, although he failed to provide a time frame for his return.
“It’s disappointing but the boys have to train, they have to prepare for the season. It happens. If you’re going to play with your feet, it can happen,” said Cheika, speaking after the Tigers’ 32-29 win over Saracens on Saturday.
“I don’t know the full extent of what happened. But all I know is that Ollie Chesum is a warrior.
“He will already be planning his return, regardless of when it is. I’m sure he’ll be back with a vengeance.
“Once I get a chance to see it, I’ll know a little more, but these things happen.”