Red Wings general manager Ken Holland told the Detroit Free Press that Green "hasn't had a lot of energy," which led to him getting blood work done and then a follow-up appointment with a doctor.
"We don't really know the extent of exactly what he has got," Holland told the newspaper, adding that the virus is attacking Green's liver. "But we are shutting him down pending what information we get from a specialist."
It's a significant early-season loss for a Red Wings team looking to get back into the playoffs after a two-year absence.
Green, who turns 33 next month, was considered one of the top free-agent blueliners this offseason before signing a two-year extension with Detroit.
He put up eight goals -- seven on the power play -- and 25 assists for 33 points in 66 games before his 2017-18 season was cut short by a neck injury that led to surgery.
He was cleared for contact before training camp began and was expected to join the Red Wings late in the preseason for games.
Green has 142 goals and 322 assists for 464 points in 787 regular-season games with Detroit and Washington, with whom he was a two-time runner-up for the Norris Trophy as the NHL's top defenseman.
Information from The Associated Press was used in this report.