Under the terms of the deal, the French bank will pay around $200 million to the Libyan government for the stake and will have an option to up its shareholding to 51 per cent in three to five years.
The sale comes as Libya's Central Bank is undergoing a privatisation with a view to changing the structure of the country's banking industry.
Meanwhile, BNP Paribas' investment in North Africa follows moves from a number of French banks to reduce their reliance on domestic market, where growth has stagnated.
The banks are also seeking new investment opportunities owing to increased competition in Eastern Europe.
Over the last two years, BNP Paribas has opened 125 outlets in Algeria, Tunisia, Egypt and Morocco.