One player from the Motherwell Rugby Football Club has already been declared dead in the weekend incident in the south-eastern coastal city of Port Elizabeth and the other five are classified as missing.
"The five are definitely presumed to be dead by now," Gordon Smart of the Coastal Water Rescue Squad told Reuters on Monday.
Authorities dispatched helicopters and boats to search for the missing players, who were preparing for an Easter tournament. They were thought to have been swept out to sea by a rip current.
"To have their afternoon turned into a day of tragedy is shocking for the whole rugby community and our thoughts and prayers go out to their families," the president of the South African Rugby Union, Oregan Hoskins, said in a statement.
Team manager Mncedisi Mazomba explained that some players showered while others went into the sea: "Next thing we know, a lady is alerting us that there were some people drowning.
"We immediately went to alert the lifesavers and were told that the rescue boat could not be dispatched because it was apparently deflated.
"That's when our guys stepped in and tried to rescue their team-mates themselves, but they were also drawn in by the strong current and were washed away."
Lifeguards were able to rescue 15 people, many of whom were later treated for shock. One man died on the beach and the search continues for the five missing players.
Brendon Helm, one of the lifeguards on duty, told newspaper Die Burger: "It is something I will always remember.
"Only eight of us and 21 desperate people with wide open eyes begging to come out. Some of us took out two or three at a time and almost got into trouble ourselves."