The Australian actor said on Twitter he had mild symptoms, including a scratchy throat and runny nose, and that as soon as he was cleared he would be back on stage.
Producers said performances would be cancelled through January 1.
Jackman tested positive after his co-star Sutton Foster came down with the coronavirus last week and was replaced by an understudy.
Foster will return on January 2 but Jackson is expected to be out until January 6.