"I would like to introduce all y'all to Jenney Shamash," the Emmy Award winner from Tasmania wrote.
"She is a producer extraordinaire. She is very funny and is really talented at reciting facts. It is a joy to behold.
"We got married in January and we are very chuffed about it. For the record: this is me gushing.
"I am full of very positive feelings. This is a nice story. My heartfelt thanks to everybody who voted for marriage equality."
Same-sex marriage was legalised in Australia in December 2017 after citizens voted for it, so her caption likely suggests that the star got married in Australia.
It is likely that Hannah met her wife through comedy as Jenney was a producer on her show Douglas, which was a follow-up to her Netflix hit Nanette.
The show is named after Hannah's dogs, and was filmed in Los Angeles in February.
The synopsis of the show explains how Hannah took Douglas "for a walk across the planet, finishing up in Los Angeles, and recorded her second stand-up special".
The show was nominated for two Primetime Emmys in 2020.
In 2019, Hannah won an Emmy for Outstanding Writing for A Variety Special as well as a prestigious Peabody award – each for Nanette.
