The women's quarter-finals were interrupted twice before Latvian Jelena Ostapenko and Swiss Timea Bacsinszky booked their semi-final places.
As a result of Tuesday's downpours, officials decided to reschedule the first two men's quarter-finals.
That means all four men's last-eight matches will be played on Wednesday.
Fourth seed Nadal meets fellow Spaniard Pablo Carreno Busta as he aims to move a step closer to a record 10th title at Roland Garros.
Twelve-time Grand Slam winner Djokovic, who is seeded second, plays Austrian sixth seed Dominic Thiem.
World number one Andy Murray faces Japan's eighth seed Kei Nishikori, while Swiss third seed Stan Wawrinka - the 2015 champion - takes on Croatian seventh seed Marin Cilic.
The remaining women's quarter-finals are also scheduled for Wednesday.
Czech second seed Karolina Pliskova plays France's Caroline Garcia, while 2014 finalist Simona Halep - the Romanian third seed - faces Ukraine's fifth seed Elina Svitolina.
Rafael Nadal and Novak Djokovic's French Open quarter-finals were postponed until Wednesday following torrential rain in Paris.