The victims were abducted in Taiz.
It was the latest attack targeting foreigners in the impoverished Arab state, where the government is struggling to restore law and order since a power transfer deal in late 2011 saw former President Ali Abdullah Saleh hand over to his deputy following months of pro-democracy protests.
The source said the gunmen seized the man and woman believed to be in their 30s in Yemen’s commercial hub to the south of the capital Sanaa, and led them to an unknown location.
“Police are trying to determine the identity of the kidnappers and where they have taken their captives to,” the source said.
The source added that the kidnappers had apparently mistaken the South African pair for Europeans or Americans but gave no further details on what they were doing in Yemen.
Kidnapping of foreigners in Yemen is common, often carried out by disgruntled tribesmen seeking to press the government to free jailed relatives or to improve public services, or by Islamist militants linked to al Qaeda.
Earlier this month, tribesmen briefly kidnapped three employees of the International Committee of the Red Cross — a Swiss, a Kenyan and a Yemen-in the southern province of Abyan but freed them three days later.
Yemen has been grappling with an Islamist insurgency, a separatist movement in the southern part of the country and a spate of attacks by gunmen on power stations, electric grids and oil pipelines since President Abd-Rabbu Mansour Hadi was elected for a two-year interim period in 2013 after Mr. Saleh stepped down.
Lawlessness in the poor Arabian Peninsula state has alarmed neighbouring Saudi Arabia, the world’s leading oil exporter, as well as the U.S., which increasingly views Yemen as a frontline is its struggle against al Qaeda.