The washout means Zimbabwe get one point, putting them second in Group B on five points, one behind leaders Sri Lanka, who beat Australia by eight wickets on Monday to secure their place in the next stage.
Zimbabwe stunned 2021 champions Australia by 23 runs last week - repeating their feat of the inaugural edition of the tournament 19 years ago - to leave the Australians in a precarious position.
The toss scheduled for 14:30 local time (0900 GMT) had to be delayed with the covers still on at the Pallekele International Cricket Stadium, before officials ruled three hours later that no play would be possible.