The men’s triathlon was due to start at 07:00 BST on Tuesday, with the swimming leg taking place in the River Seine.
But after swimming training for triathletes was cancelled on Sunday and Monday, tests revealed the water quality still did not reach the required standard.
Heavy rainfall in Paris on Friday and Saturday has caused the water quality to diminish and the men’s race has been put back to Wednesday at 09:45 BST.
The women’s event is due to start at 07:00, but organisers say both races only have a 60% chance of going ahead.
Friday remains a back-up date for both races and, as a last resort, organisers say the event could be contested as a duathlon – just the cycling and running legs.
The surfing is being held in Tahiti, French Polynesia, and Tueday’s sessions have also been postponed, due to adverse weather conditions.
The events were scheduled to begin at 18:00 BST. Technical delegates are set to decide on the next sessions at 18:45.