Mandla Mandela, an ANC member of parliament and head of the Mandela family clan, allegedly missed three payments to his estranged wife, Tando Mabunu-Mandela, the weekly newspaper City Press reported on its website.
The publication reported that a maintenance investigator said Mandela had refused to accept a summons given him on July 11.
The court granted an order to deduct the sum from Mandela salary, and issued the arrest warrant after his failure to appear in court, the newspaper said.
Mandla Mandela, 38, is going through a complex divorce with his first wife. He has drawn wide attention for marrying two other women apart from her in recent years.
While polygamy is legal under tribal law, a man cannot have different wives under both tribal law and under civil law.
Mabunu-Mandela has appealed successfully to the courts to rule against the other marriages.
Mandla Mandela has also garnered headlines after neighbours accused him of expropriating village land to build a luxury hotel and sports stadium, and a court had to order him to release journalists he held hostage when they investigated the allegations.
Nelson Mandela, now 94, was elected the country’s first black president in South Africa’s first all-race vote in 1994 and served one term before stepping down in 1999.