The first four occasions were related to triathlon events in the French capital, with the men's triathlon postponed by a day.
The Seine has been the focus of attention during the Games, consistently failing water quality tests despite a 1.4 billion euro upgrade to improve the Paris sewerage and water treatment systems.
Organisers issued a statement early Tuesday saying the marathon swimming "familiarisation session" would not go ahead.
"After the daily situation meeting this morning between Ville de Paris, Paris 2024 and World Aquatics, it has been decided that the familiarisation session to take place today, 6 August 2024 is cancelled," the statement said.
Several triathletes had expressed frustration over the repeated cancellations and uncertainty.
The River Seine was judged clean enough to stage the mixed triathlon relay on Monday following uncertainty over pollution levels and illness in the build-up.
The race turned out to be a thriller, Germany's Laura Lindemann holding off a fierce challenge from the United States and Britain to take gold.
The women's 10-kilometre marathon swim is due to take place early Thursday, with the men's event listed for the following day.