Konta, ranked 18 in the world, lost 6-4 7-5 to China’s Zheng, who is 44 places below her in the world rankings.
The Briton needed a medical time out three games into the second set for a “Niggle” on her pelvis.
But following the match, Konta said she expected to play in the Wimbledon warm-up events in Birmingham and Eastbourne.
Konta’s defeat leaves qualifier Tara Moore as the only remaining British player in the competition.
She takes on world number 67 Christina McHale at about 17:00 BST on Thursday.
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