Mbacke was the fifth caliph of the Mouride and the last surviving son of Ahmadou Bamba Mbacke, who founded the group in 1883.
He was buried in the holy city of Touba, about 200km east of the capital, Dakar, in a ceremony attended by Wade according to a source in the presidency.
News of the death was delayed until after the burial ceremony so as to avoid disruption from mourning followers of the brotherhood.
The brotherhood is the biggest centre of religious, economic and political influence in the mainly Muslim country.
|The Mouride wealth has seen Touba grow
into Senegal’s second-largest city [EPA]
Although Senegal is a secular country, the majority of its democratically elected rulers have had to seek the endorsement of Mbacke.
His image can be seen widely on the dashboards of taxis and in the homes of his millions of followers.
Followers waited in long queues to visit the grave, within the grounds of Touba’s Grand Mosque.
“We’ve lost him, we’ve lost everything,” said Mamadou Diouf, a 32-year-old mechanic who rode from Dakar on his moped as soon as he heard the news.
Among Mbacke’s achievements was the transformation of Touba from a rural outpost into Senegal’s second-largest city with a population of one million.
Touba was founded by Mbacke’s father, who died in 1927, and has often been described as a state within a state.
Inside the city visitors cannot drink, smoke or dance.
The Mouride is one of several brotherhoods in Senegal, centred on allegiance to the teachings of its founder and his scions and a particular interpretation of the Quran.
The movement became wealthy based on Mbacke’s investments in agriculture, particularly in peanuts.
Mbacke had built several Islamic schools in Senegal and figured among the 100 most influential Africans in a list drawn up by the French magazine Jeune Afrique.
His father aided in the mass conversion of the ethnic Wolof people from tribal paganism to Islam before founding the Mouride.
Many Senegalese looked to the organisation for leadership in the fight against French colonial authorities.
Bamba’s eldest grandson will become the sixth caliph of the Mourides.