He was in his late 60s.
The bluesman from Mali was among West Africa's most internationally successful artists, winning acclaim around the world for his 1994 album Talking Timbuktu, recorded with Texan guitarist Ry Cooder.
"Ali was for Mali, for Africa and for the rest of the world a very great musician. A musician who leaves behind him a fabulous heritage," said Mali’s Culture Minister Cheick Oumar Sissoko.
Dubbed "the African John Lee Hooker", Farka Toure was born in 1939 but did not know his exact date of birth.
He won his second Grammy just last month for In the Heart of the Moon, recorded with his countryman Toumani Diabate and had just finished work on a new solo album when he died.
Multi-lingual performer
His haunting music, which he sang in 11 languages, combined the traditions of his native northern Mali with the influence of American blues, which he saw as having its roots in West Africa.
Radio stations throughout Mali interrupted their programs to broadcast his hypnotic desert blues.
Though he achieved international renown, Farka Toure remained deeply rooted in the traditions of his home region, near the famous Saharan trading town of Timbuktu.
He retreated from music in 1990 to concentrate on his rice farm in the village of Niafunke. When his producer convinced him to record again, an impromptu studio running on generators had to be set up there so he could tend his fields at the same time.
Farka Toure was appointed mayor of Niafunke in 2004 for his efforts to improve the lives of those in the region. He cultivated more than 300 hectares of land around the village, where he will be buried, and set up welfare projects for women and children.
Farka Toure, who took up the njurkel - a traditional type of lute, at the age of 10, occasionally toured in North America and Europe, adapting influences from jazz, blues and the traditions of West Africa's Songhai, Mande and Tuareg cultures.
He was fiercely proud of his native country, Farka Toure never allowed outside influences to dilute his musical heritage.
"We were in the middle of the landscape which inspired the music and that in turn inspired myself and the musicians. My music is about where I come from and our way of life," Farka Toure was quoted as saying of his 1999 album, Niafunke.