Green, 33, missed the beginning of the season because of the virus, which was attacking his liver.
After the latest flare-up, he saw a specialist who recommended multiple weeks of rest. Coach Jeff Blashill said he was told that while Green does not face any long-term implications, he needs proper rest to address the issue.
Green bounced back from the virus during the season, registering 26 points in 43 games before the virus returned.
He is under contract for one more year after this one, with a cap hit of $5.375 million.
The Red Wings have lost eight games in a row and are tied for the second fewest points in the league.