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New Zealand lead Sir Ben Ainslie's Great Britain team 3-1 in their first-to-five contest. In the other semi-final, Japan lead Sweden 3-1.
America's Cup Race Management said all four scheduled races will now move to Thursday, when better conditions are forecast.
"It's not good out there today," said regatta director Iain Murray.
"Unfortunately we won't be racing and we will have to come back tomorrow."
The delay could benefit New Zealand, who spent all night repairing their catamaran after a spectacular capsizing during a race against Britain on Tuesday.
The catamaran fell forwards on the run-in to the start, leaving some crew suspended in the hull above the water.
Three were thrown overboard but all of New Zealand's crew were accounted for.
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Wednesday's semi-final races at the America's Cup in Bermuda have been postponed because of high winds.