Top seed Williams, seeking to become the first woman since Steffi Graf in 1988 to complete a rare calendar Grand Slam, will face the tall, big-hitting Bertens in the third match of the day at Arthur Ashe Stadium.
A well-rested Williams, who needed only 30 minutes to win her first-round match when her opponent retired with a knee injury, will start a prohibitive favourite against her 110th-ranked opponent from the Netherlands.
It will be the first career match-up between Williams and Bertens.
Defending men's champion Marin Cilic, the ninth seed, will also be in action as he faces Russian Evgeny Donskoy.
In other men's action, top seed Novak Djokovic will cap the night session when he battles unseeded Austrian Andreas Haider-Maurer under the lights.
Serbian Djokovic dropped only three games in a first-round canter, but might get a tougher contest from world number 52 Haider-Maurer, who downed Canadian Vasek Pospisil in five sets on Monday.
Eighth seed Rafa Nadal, who survived a dangerous first-round opponent in Croatian Borna Coric, will be up against unseeded Argentine Diego Schwartzman in a daytime match in the Louis Armstrong Stadium.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Frank Pingue)
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