Kerber, who nearly ended Serena Williams' long run as world number one last month in Cincinnati, tries to stay on track for a possible winner-take-all match with the American in the finals when she goes against Roberta Vinci.
The German, who won the 2016 Australian Open and was runner-up to Williams at Wimbledon, has yet to drop a set at Flushing Meadows.
The seventh-seeded Vinci could be a difficult hurdle for Kerber. The Italian, last year's U.S. Open runner-up , has split four career matches with Kerber and won two of three on hard courts.
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The other women's quarter is a battle of none seeds with former world number one Caroline Wozniacki playing Anastasija Sevastova of Latvia, who upset French Open winner Garbine Muguruza and Britain's 13th-seeded Johanna Konta along the way.
Men's world number one Djokovic, who has hardly been tested after receiving a second-round walkover and benefited from a first-set retirement in the third round, faces French veteran Jo-Wilfried Tsonga in his quarter-final.
The Serb leads their head-to-head 15-6 and has won 11 of his last 12 matches against Tsonga dating back to 2012. Tsonga's wins include a five-set quarter-final victory over Djokovic at the 2010 Australian Open.
The other men's quarter on Tuesday is an all-French affair with 10th-seeded veteran Gael Monfils taking on 22-year-old Lucas Pouille, who shocked 14-times grand slam singles winner Rafa Nadal in five sets in the fourth round.
(Editing by Steve Keating.)
