Svetlana Gomboeva, 23, collapsed while checking her scores. She regained consciousness and left on a stretcher.
Earlier this week experts said Tokyo's heat and humidity could pose a significant threat to competitors.
Monday's rowing races have switched to Sunday to avoid "unrowable" conditions.
The Japanese Environment Agency has issued heatstroke alerts, warning the public not to exercise outside.
With temperatures of around 33C in the archery dome on the sport's first day of competition on Friday, athletes had challenges with hydration and staying cool, while support staff huddled in shaded areas.
"It turns out that she [Gomboeva] couldn't stand a whole day out in the heat," said Russian Olympic Committee coach Stanislav Popov.
"This is the first time I remember this happening. In Vladivostok, where we were training before this, the weather was similar. But humidity played a role here."