The award-winning hip-hop dancer - who has worked with chart-toppers Justin Bieber, Rihanna, Janet Jackson, Jennifer Lopez and Nicki Minaj - announced the news in a message on Saturday.
She wrote: "My fingers are numb, my heart beat is slow. Today I feel pain, all over my soul. It's hard to believe my munchkin is gone.
"But your song I will sing as I try carry on. You are needed in heaven, so fly away, I will be missing your kisses every day."
On Instagram, Goebel also thanked fans for their "uplifting messages of love".
Goebel was in New York earlier this week after receiving three nominations at the MTV Music Video Awards. She also choreographed Rihanna's opening dance routine.
Her nominations were for her work on Justin Bieber's video for the single Sorry.
Prior to the awards, she tweeted: "This is crazy ... this is such a beautiful reminder to myself that anything is possible.
"Don't give up on your dreams, if this Polynesian high school drop out from Auckland NZ can do it ... you can do it too."