They were believed to have been involved in the development of the hotel from which they were abducted on Monday, said spokesperson Clayson Monyela.
"The details are sketchy, but partly, they are thought to be involved in a hotel development dispute between the landlord and the people involved. That's what we have been told," he said.
"We have confirmed that they are South Africans, and we are sending our ambassador to engage with authorities tomorrow [on Wednesday] to intervene and assist."
Previously, the French news agency Agence-France Presse quoted an official as saying the kidnappers came from the Janadiyah area, 35km east of Taiz.
The official told AFP the kidnappers belonged to a local chief, who had had a long-running dispute with the authorities about a plot of land, and that it was possible the tourists were being used for bargaining.