The New York-based singer won the award for her Orchestre Philharmonique du Luxembourg collaboration, Sings.
"I want to dedicate this Grammy to all the traditional musicians in Africa, in my country, to all the young generation," Kidjo said.
Her album beat one by Malawi's Zomba Prison Project and South Africa's Ladysmith Black Mambazo.
Kidjo, one of Africa's most prominent musicians, has now won the award for the second consecutive year.
The album merges African song writing and rhythms with European classical instrumentation, a fusion on which Kidjo has repeatedly experimented.
Kidjo described the album as an artistic challenge as traditional African bands follow the lead of the soloist much more closely, unlike Western orchestras that generally play off refined scores.
The singer, who has worked for a long time with Philip Glass, a leading US composer, said Africa was on the rise.
"Africa is positive, Africa is joyful," she said after collecting the award.
The 55-year-old singer added that she has been fighting for a positive image of Africa for a long time and believed music could connect the world and served as a tool for peace.
She later told the BBC: "I have to continue to working...  to open the way for many artists from Africa to come."
African-American rapper Kendrick Lamar won the most prizes on the night with five awards.
The 29-year-old performed The Blacker The Berry, walking on stage as part of a chain gang from inside a prison, before transitioning to Alright, in front of a huge bonfire and African dancers.
His performance ended with the unveiling of a new track with Lamar in front of a map of the African continent and the word "Compton" - his hometown in California - written on it.
Benin's Angelique Kidjo has won the best world music album of the year at this year's Grammys in Los Angeles.