In the video, Jackman is seen wearing a black facemask and delivering the message against a white wall as he reassured fans.
"Hey good morning, so I just wanted you to hear it from me that I tested positive this morning for Covid," he said.
"My symptoms are like a cold, I have like a scratchy throat and bit of a runny nose but I'm fine. And I'm just gonna do everything I can to get better ASAP.
"And as soon as I'm cleared I'll be back on stage heading to River City. So just wanted you to hear from me. So please stay safe, be healthy, be kind."
The 53-year-old began starring in The Music Man on Broadway before Christmas but just days later his co-star Sutton Foster came down with Covid.
Now, with its second lead in isolation, the production has cancelled all performances until New Year's Day with Jackman out of action until at least January 6.
New York is currently in the midst of a major Omicron surge.