The collective - fronted by singer Florence Welch - will put out the live LP on April 9.
The 11-track collection will be recordings of her New York gig last December, which she played with a 10-piece gospel choir.
The set includes covers of 'Try A Little Tenderness' and 'Jackson' - a duet with Queens of the Stone Age rocker Josh Homme.
Previous acts to have released an MTV Unplugged album include Nirvana, Lauryn Hill, Oasis, Alicia Keys and Paul McCartney.
The band recently announced details of their new single 'Never Let Me Go', the third cut from their latest album Ceremonials.
> Florence + the Machine "really anxious" to write third album
The tracklist for MTV Unplugged - A Live Album appears below:
1. Only If For A Night
2. Drumming Song
3. Cosmic Love
4. Breaking Down
5. Never Let Me Go
6. Try A Little Tenderness
7. No Light No Light
8. Jackson (feat. Josh Homme)
9. What The Water Gave Me
10. Dog Days Are Over
11. Shake It Out
Listen to a live performance of 'Never Let Me Go' below: