Born in 1953, Vall served as the head of a transition government that handed over to Mauritania's first democratically elected president, Sidi Ould Cheikh Abdallahi.
Vall led a 2005 coup against dictator Maaouiya Ould Taya, but kept a promise to step aside for elections two years later.
President Mohammed Ould Abdel Aziz announced three days of mourning, the Mauritanian Information Agency (AMI) said, while a family source confirmed to AFP he had fallen ill and had a heart attack.