Slovakian star Rybarikova was defeated by Barbora Strycova in Austria in the 2017 final, but the seventh seed will not challenge this year after losing 6-3 6-4 to Van Uytvanck on Monday.
Sixth seed Anastasia Pavlyuchenkova - the 2015 champion - fared better as she progressed to the last 16.
Viktoria Kuzmova was edged out 7-5 7-5 by the Russian in the first match of the main draw.
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