"We can confirm that the extradition request has been duly submitted to the United Arab Emirates' central authority today," Ronald Lamola told reporters.
South Africa had 60 days to submit the request, after Dubai police arrested the Guptas in June.
The brothers are accused of using their connections with Zuma, head of state from 2009 to 2018, to win contracts, influence cabinet appointments and siphon off state funds. Zuma and the Guptas have denied all wrongdoing.
South Africa's National Director of Public Prosecutions Shamila Batohi said the extradition process could take several months, declining to give a more precise timeframe.
She said the National Prosecuting Authority (NPA) viewed the submission of the extradition request as an important milestone in attempts to hold accountable perpetrators of corruption.
"What I want to assure the people of South Africa is that as the NPA we do not bring cases unless we ourselves are satisfied that it meets the standard of reasonable prospects of a successful prosecution," she said.
Dubai police arrested the Guptas on the basis of an Interpol "red notice," a request to law enforcement officials worldwide to locate and provisionally arrest someone pending extradition.
The UAE ratified an extradition treaty with South Africa in April 2021, a move that the South African government hoped would lead to the return of the Guptas to face charges.
Reuters, the news and media division of Thomson Reuters, is the world's largest multimedia news provider, reaching billions of people worldwide every day.Go to: https://www.reuters.com/