Ould Mohamed Saleh holds a degree in economics from the Faculty of Law and Economics of Tunis, a diploma of advanced studies (DEA) in economics (development economics) from the University of Paris I Panthéon-Sorbonne (France) and a diploma awarded in Paris by the National School of Administration (ENA) at the end of an international cycle of public administration.

He began his career in 1985 as Head of the Projects Service, before becoming Deputy Director of Finance and External Debt at the Mauritanian Ministry of Economy and Finance, from 1988 to 1989. From 1989 to 1991, he held the post of Principal Advisor to the Ministry of Planning and Employment and from 1991 to 1992, that of Director of Planning responsible for the coordination and formulation of economic development programs within the same ministry. From 1992 to 1997 he was Economic Advisor to the Prime Minister, then in 1997 he was appointed Minister of Fisheries and Marine Economy and in 1998 he became the first Commissioner for Human Rights, the fight against poverty and reintegration within the framework of the newly created eponymous Commission in Mauritania.

Ould Mohamed Saleh joined FAO in 2003 as the Organization's Representative in Lebanon, before becoming Representative in Togo in 2006. From 2008 to 2010, he served as Deputy Regional Representative for the Near East and of FAO Representative in Egypt. In 2010, he was appointed Director of the FAO Liaison Office with the United Nations in Geneva, then Regional Representative for the Near East on September 30, 2012.

Abdesselam Ould Mohamed Saleh was appointed Minister of Petroleum, Mines and Energy of the Islamic Republic of Mauritania in August 2020.