The two have 2-year-old boys, Taane Diamond and Barry Kowhai.
Moa and Fyfe - a burlesque dancer also known as Azaria Universe - became the poster couple for gay marriage equality and celebrated a civil union in February 2010.
Moa, 33, declined to comment on the break-up, which has come at the end of what she had earlier described as a tough year.
She had previously written about the stresses of parenthood "exploding like a sad bomb"around her. She said she had "learned the hard way"how difficult it was having children, especially twins. It is understood the split is amicable, and she and Fyfe are sharing the care of their sons.
Twin boys Taane Diamond and Barry Kowhai.
The couple met after Moa saw Fyfe perform burlesque on stage in Melbourne. Both described it afterwards as love at first sight.
"I fell in love instantly and that was it. I knew I was going to be with her for the rest of my life. I've never loved someone as much as I love her. I idolise her," Moa said.
Fyfe was the inspiration behind many of the songs on Moa's 2010 album Love in Motion. It had the dedication words, "For Azaria, let it be you, I fall into"inside the cover.
Her new album, Songs for Bubbas, was released last week.
The pair became parents in July 2011 after Fyfe had one round of IVF treatment. The donor father is believed to be Moa's brother.
Just last week Moa told the New Zealand Herald she was happy with her life. "This is the time in my life when I have it all - good music, great friends, a fantastic family and two amazing sons. What more could I want?"
- by Kirsty Wynn of the Herald on Sunday
