The umpires called off the scheduled third day’s play, without a ball being bowled, during the lunch break as incessant rain left large puddles of water on the outfield at the Chinnaswamy stadium.
The entire second day’s play was also abandoned on Sunday and more wet weather is forecast over the southern city, caused by a cyclonic depression over the Bay of Bengal.
On the rain-free first day, South Africa were shot out for 214 after being sent in to bat in overcast conditions and India replied with 80 for no loss by stumps.
India lead the four-match series after securing a 108-run win in the first Test in Mohali last week.
The third Test is to be played in Nagpur from November 25.