New Idea reported McCune was shocked by the emergence of the video but her representatives declined to comment.
The Gold Logie-winning actress, 43, is starring with Rhodes in the Australian musical production of The King and I in Melbourne.
The pair struck up a relationship after co-starring in South Pacific in 2012. They were both married at the time and were photographed kissing and cuddling in public outside a coffee shop in Melbourne.
Both have refused to discuss their relationship but the former Christchurch star said this year that he understood the couple's chemistry made them attractive for The King and I producer John Frost to cast.
"I think that's what makes it work - the chemistry is really important. We'll leave it at that," he said.
McCune married Tim Disney in 2000. They have three children together.
- Staff reporter, agencies