Play was suspended on Tuesday just before 1530 local time (1330 GMT) during the first two women's quarter-finals at Roland Garros.
Jelena Ostapenko was serving for the second set in her match against Caroline Woznacki after the Dane clinched the opener 6-4.
Timea Bacsinszky was a set up on France's Kristina Mladenovic on Court Philippe Chatrier, with a resumption not expected before 1830 (1630 GMT).
Nine-time champion Nadal is due to take on compatriot Pablo Carreno Busta, while title-holder Djokovic faces sixth seed Dominic Thiem in a repeat of last year's semi-final.
As a result of the downpours, all four men's quarter-finals will be played on Wedneday with Andy Murray against Kei Nishikori and Stan Wawrinka facing Marin Cilic.