Extradition talks are taking place with the UAE, South African officials say.
The brothers fled South Africa after a judicial commission began probing their involvement in corruption in 2018.
They are accused of paying financial bribes in order to win lucrative state contracts and influence powerful government appointments.
The family moved from India to South Africa in 1993. They also face accusations of money laundering in India, where tax officials raided properties belonging to them in 2018 in multiple cities, including their company office in capital Delhi.
Many of the most serious corruption allegations levelled against the Indian-born brothers focus on their relationship with Jacob Zuma, who was president of South Africa from 2009 until he was forced to step down amid a storm of corruption allegations nine years later.
The Gupta family is accused of using their close links with Mr Zuma to wield enormous political power across all levels of South African government - winning business contracts, influencing high-profile government appointments and misappropriating state funds.
Mr Zuma and the Guptas deny any wrongdoing.
After the brothers fled the country, South Africa negotiated an extradition treaty with the UAE in 2021.
President Cyril Ramaphosa's government has said it hoped the agreement would lead to the return of the Guptas to face charges, but it was not immediately clear following the arrests whether the brothers will return to South Africa.
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