Green is not expected to be ready for the regular-season opener Sept. 8 at Seattle.
He was carted off the field Saturday during the Bengals' first training camp practice of the season at Welcome Stadium in Dayton, Ohio.
The Bengals were practicing at Welcome Stadium as part of the NFL's 100th anniversary celebration. The conditions of the field were considered subpar, but the Bengals cleared the football field for use in the end, a source told Schefter. The remainder of the Bengals' training camp practices will be in Cincinnati.
On Sunday, Bengals wide receiver Tyler Boyd described the field conditions in Dayton as "terrible."
"The turf was terrible. I couldn't run any routes out there. I'm falling all over the ground. It was bad. It was rocks, pebbles out there. Man, it was somewhere we shouldn't have been. I'm not trying to say any excuses, but it is what it is," Boyd said.
Bengals coach Zac Taylor, however, said the field shouldn't be blamed for Green's injury.
"I don't think the turf had anything to do with it," Taylor said at the end of Sunday's practice.
Triangle Park in Dayton was the site of the first NFL game, between the Dayton Triangles and Columbus Panhandles in October 1920.
Green's left shoe was removed before he departed the field. Last season, he missed seven games because of a right toe injury.
That campaign marked only the second time Green did not have at least 1,000 receiving yards in a season during his eight-season career. Green, a seven-time Pro Bowl selection, participated in Bengals minicamp in June.
Green, who turns 31 this week, missed only four games in his first five NFL seasons, but he has missed 13 games in the past three seasons.
He is entering the final year of his contract.
ESPN's Ben Baby contributed to this report.