Wickmayer was brushed aside 6-4 6-3 by qualifier Casey Dellacqua in the second round.
There were no such problems for the other seeds ahead of the US Open - with Jelena Jankovic, Roberta Vinci, Peng Shuai, Chanelle Scheepers and Sorana Cirstea all advancing.
Former world No.1 Jankovic, the second seed, beat Arantxa Rus 7-6 (7/5) 6-2, while third-ranked Vinci overcame Polona Hercog 6-2 6-3.
Jankovic will now face Cirstea after the eighth seed recorded a 6-1 7-5 victory over Alize Cornet, with Vinci's reward a quarter-final clash with seventh-seed Scheepers, a 6-4 7-6 (7/3) winner over Marina Erakovic.
Sixth seed Shuai saw off Pauline Parmentier 6-4 6-2 and will now go up against Serbian wild card Bojana Jovanovski, a 7-6 (7/5) 6-2 victor against Mirjana Lucic.
Aleksandra Wozniak also advanced to the last eight after a 6-2 6-2 win against Eugenie Bouchard, with Dellacqua next up for the Canadian.