The cover, which appears below, sees the singer dancing in front of a fire on the beach.
Discussing the song, Furtado said: "It's an ode to the spirit which resides in all of us and triumphs over anything.
"It is inspired by people I have met, and special moments in history that I have read about. Spirituality is one of the underlying themes on the album."
The track - produced by Rodney 'Darkchild' Jerkins (Michael Jackson, Britney Spears) - follows 'Big Hoops (Bigger The Better)', which peaked at number 14 on the UK singles chart.
'Spirit Indestructible' also serves as the title track from her forthcoming album, which is due out September 17 and a day later in the US.
Watch a live performance of the song below:
