Cherry was born Neneh Mariann Karlsson, to a Sierra Leonean father, drummer Amahdu Jah and a Swedish painter/textile artist mother, Monica Karlsson, known as Moki Cherry. Her siblings include the singers Titiyo Jah  and Eagle-Eye Cherry. Her step-father Don Cherry helped raise her since birth[citation needed] so Neneh took his surname. Cherry lived the first years of her life in the small English town Pudsey. Regarding her childhood, Cherry said:

My mother is Swedish and she's an artist. She's an amazing lady. When I was a baby and she was going to design school, she used to take me along in a basket!

Soon Moki met Don and the family accompanied him on his tours through Europe and North America. In the early 1970s the Cherry family nestled into a small apartment on East 9th Street in New York City. Moki died in 2009 in Sweeden, though before she was living In L.I.C. New York. Cherry married The Bank drummer Bruce Smith in 1983 and their daughter Naima was also born that year.  

They divorced in 1984. In 1987 she met producer Cameron McVey at Heathrow Airport. Cherry and Cameron were en route to Japan as fashion models as part of London designer Ray Petri's Buffalo Posse. Cherry proposed, and the two married in 1990. Together they have daughters Tyson, born in 1989, and Mabel, born in 1996.  Their relationship is also work-related, as McVey produced and co-wrote Raw Like Sushi; together they have supported a variety of heavyweight British acts; and they are in the group cirKus together.

In 2004, Cherry became a grandmother when her 19-year-old daughter Naima had son Louis Clyde Flynn Love.

The Cherry-McVeys have lived throughout Europe. In 1993 they moved to Spain. In 1992, they briefly attempted to live in New York. They bought a home in the Park Slope section of Brooklyn, New York. Soon after moving in, the couple was held up at gunpoint and robbed by a teenage bandit. The entire family packed up again and headed back to London's Primrose Hill.  

They next returned to Cherry's childhood home in Tågarp, Sweden; living in the same schoolhouse-turned-home (featured in Homebrew album artwork) that Cherry studied in as a child.  Currently they split time between their country house near Birmingham and Wolverhampton  and London.

Cherry has stated in interviews she is bisexual.