John and Lynette Rodgers, from Holywood in County Down, were found on a beach at Plettenberg Bay in the Western Cape on Friday.
Efforts were made to resuscitate them, but they were declared dead at the scene.
Rescue workers said sea conditions were rough at the time, with strong rip-currents in the water.
It is believed they had gone for a swim shortly after arriving at the popular tourist resort.
A local man raised the alarm at about 18:00 local time after discovering the body of Mr Rodgers, 28, in shallow surf on Robberg Beach, the National Sea Rescue Institute said.
Two women walking along the beach found the body of Mrs Rodgers, 26, about 200 metres away.
Rev Stephen Lowry of First Holywood Presbyterian, the church where the couple were married, said: "The happiness and joy of their wedding last Saturday has been replaced by grief and loss."
The UK Foreign Office said it was providing assistance to both families "at this extremely difficult time, and will remain in contact with local authorities".
A couple in their 20s from Northern Ireland has drowned while on honeymoon in South Africa.