An aircraft, chartered by the prominent Gupta family, which has close ties to President Zuma, landed at the restricted Waterkloof Air Base in Pretoria on Tuesday.
The aircraft carried about 200 people en route to Sun City for the wedding taking place this week.
International Relations spokesperson Clayson Monyela said preliminary investigations show no permission was given for the airplane to land at the military airbase, state-owned broadcaster SABC reported.
"And that's why this decision has been take so that all these matters can be probed around circumstances in which they were able to secure this flight clearance allowing this plane to land there, when it should not have because that's a military facility, no civilian plane should be landing," he said.
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Local radio reported that the Guptas' wedding guests were flown to the base and escorted from there by blue-light vehicles to Sun City, in North West.
The wedding, billed as 'the South African wedding of the century', also has Bollywood actors and singers flying in for an extravagant celebration.
Yesterday, the Gupta family said permission to land at Waterkloof was obtained through the Indian High Commission. They said the High Commission had applied for permission for the plane to land at the base, because the delegation included government ministers.
Meanwhile, the minister in the Presidency Collins Chabane said today that President Zuma is not going to attend the lavish Gupta wedding at Sun City this weekend.