Sipho Ngwema, the director of special operations for police elite anti-fraud unit called the Scorpions, said there was "credible evidence" Sir Mark had financed the coup attempt in March.
"The Scorpions have arrested the son of a prominent former British politician. We are investigating charges of contravening the Regulation of Foreign Military Assistance Act," he said.
Dozens of suspected foreign mercenaries were arrested in March in Zimbabwe and Malabo, capital of Equatorial Guinea, over the alleged plot to topple President Teodoro Obiang Nguema.
There was no immediate indication that Thatcher faced extradition to Malabo to join eight South Africans, six Armenians and four Equatorial-Guineans currently on trial there for the alleged coup attempt.
The arrest comes on the same day as a visit to Cape Town by British Foreign Secretary Jack Straw and four ministerial colleagues. British High Commission spokesman Nick Sheppard said the incident would not impact Straw's visit.