The businesswoman and Boston University graduate, 53, is the first of Mandela's three remaining children to enter public life.
The Argentinian government said it had accepted her appointment on Monday and that the appointment demonstrated "the importance of Argentina to the South African government". Bilateral trade had reached $1.3bn a year, "demonstrating the high potential for both economies", it added.
Mandela-Dlamini was a toddler when her father was imprisoned and she was not allowed to visit him in jail until she was 16. He was still in prison when she married the Swazi prince Thumbumuzi Dlamini in 1973. They have two sons and lived in Boston until their divorce.