China's Zheng has largely struggled to replicate the form that carried her to the gold medal at the Paris Games two years ago, with a chronic right elbow injury stalling her progress and forcing her to undergo surgery last summer.
The 23-year-old, who made the Roland Garros quarter-finals last year, took treatment for a foot problem midway through the second set before her first defeat in the opening round of the French Open.
World number 114 Chwalinska, who came through three rounds of qualifying and dished out two bagels along the way, showed no mercy and wrapped up the win to book a clash with either Tatjana Maria or 23rd seed Elise Mertens in the second round.