Wiseman Zimba, a cousin to David's biological father, Yohane Banda, confirmed the death in an interview to PEOPLE.
"Mama Asineti died last night," Zimba said Monday. "Burial is tomorrow."
Mwale, 60, who had looked after infant David after his birth mother died, had recently been bedridden with pneumonia.
David's biological mother, Marita, died a week after he was born in September 2005. So "Mama" helped take care of the baby with the child's father, Yohane Banda.
They later made a decision to surrender David to the Home of Hope Orphanage because the family was too poor to afford to feed him with infant formula milk.
Madonna, through her Raising Malawi – the charity she set up for her Malawi cause – found him at the facility and fostered the child. The High Court in the capital, Lilongwe, okayed the adoption on May 29 this year after a two-year interim period that also included social service visits to Madonna's home in London.
Playing with His SiblingsMwale, who wholeheartedly approved the controversial adoption – some critics claimed Madonna received preferential treatment – has died before she fulfilled her wish to see how David was faring with Madonna.
Last week, David, 2, was spotted in New York City's Central Park with brother Rocco, who turns 8 on Monday, and sister Lourdes, 11, playing with radio-controlled toy yachts in a lake.
In her last interview, given last month when David's dad's new wife, Flora, gave birth to another son, Dingiswayo, Mwale said: "I wish David would come to see me before I die. I hope he will one day come to see his brother."