The result means South Africa have earned their first point of their campaign in four outings.
Having been sent in to bat, South Africa lost Hashim Amla (6) and Aiden Markram (5) cheaply and were reeling at 29/2 when rain stopped play.
The players never took the field again, with Proteas captain Faf du Plessis saying: “Those [rainy days] are the worst. Both teams wanted to play and get a result.
“It is very disappointing, but you can’t control the weather.”
The result means South Africa now have to win their remaining five matches, with other results going their way, in order to make it to the playoffs.
That journey starts against Afghanistan on Saturday, with Du Plessis adding: “It’s our own fault, we didn’t play our best cricket so far.
“So we’ve got Afghanistan next and I hope we put on a really solid performance to build on the team’s confidence we’ve got to beat Afghanistan.”