Abraaj, which has $2.2 billion invested in Africa, did not give a value for the transaction.
Fan Milk’s operations include Nigeria, Ivory Coast and Ghana, where it owns a 56.6 percent stake in listed unit Fan Milk Ltd (FML.GH), which has a market value of $337 million, according to Thomson Reuters data.
Private firms are increasingly looking to Africa for deals, drawn by rising middle classes and growing consumer spending.
Abraaj, founded in 2002 by Group Chief Executive Arif Naqvi, has about $7.5 billion in assets.
The firm acquired UK-based specialist fund manager Aureos Capital last year, to beef up its emerging market presence, especially in Africa.
Fan Milk, which was originally set up by a Danish family in the 1950s, also has operations in Togo, Burkina Faso and Benin.