The Glasgow-born artist worked with the likes of Madonna and Charli XCX.
In a statement, Sophie's management said the musician had died at around 04:00 on Saturday in the Greek capital, where she had been living.
"Sophie was a pioneer of a new sound, one of the most influential artists in the last decade," they said.
A further statement from Sophie's record label Transgressive, explained how the "terrible accident" had occurred.
"True to her spirituality she had climbed up to watch the full moon and slipped and fell," they posted online. "She will always be here with us."
"The family thank everyone for their love and support and request privacy at this devastating time."
Sophie was also known as a transgender icon, after affirming their identity in the 2017 video for It's Okay To Cry.
The artist's management said she would be remembered "not only for ingenious production and creativity but also for the message and visibility that was achieved. An icon of liberation".