Swiatek, the world No.8, won her breakthrough grand slam title in Paris last year.
But she was no match for Spain's Paula Badosa, who won 6-3, 7-6.
According to L'Equipe tennis journalist Quentin Moynet, the 20-year-old was "inconsolable" and "in tears" after the loss, while Portuguese tennis journalist Jose Morgado tweeted that she was "crying a lot in the end".
Swiatek, who made the quarter finals at Roland Garros this year, as well as the fourth round at the Australian Open and Wimbledon, said her reaction was normal.
"Most of the players cry after losing matches, although it is not visible in the vision," she said, per polsatsport.pl.
"This time it happened to me, but we are also human. Competing at the highest level for a week is not easy. Only one person wins out of many.
"Sometimes it's a frustrating sport, but of course there is nothing to complain about."
Badosa, who also made the quarter finals in Paris earlier this year, now plays Argentina's Nadia Podoroska in the third round, while a potential quarter final against Naomi Osaka awaits.
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