Cherry was born as Neneh Mariann Karlsson, to a Sierra Leonean father, Amahdu Jah (a drummer) and a Swedish painter/textile artist mother, Monika Karlsson, known as Moki Cherry. Her siblings include the singers Titiyo Jah and Eagle-Eye Cherry. Her step-father Don Cherry raised her since birth so Neneh took his name on. Cherry lived the first years of her life in the small Swedish town Hässleholm. 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 Mokie 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 still lives in New York : either in Garden City, New York or in a loft in Queens, New York just across the East River from East 60th Street . Moki has exhibitions in major museums and galleries in New York and Stockholm.

Cherry joined Rip Rig & Panic as a singer. She 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 (1989) and Mabel (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 group cirKus together.

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

The Cherry-McVeys have lived throughout Europe. In 1993 they moved to Spain, and lived there until 1999. In 1995, 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 Hässleholm,Sweden; living in the same schoolhouse-turned-home (featured in Homebrew album artwork ) that Cherry grew up in.

Today they split their time between their country house near Malmö and Stockholm and London.