Zheng powered her way to gold in Paris last year and was tipped for a strong run at the All England Club but doubles specialist Siniakova had too much grasscourt craft.
Siniakova, three-times women's doubles champion at the All England Club, took the opening set when Zheng netted a backhand.
Zheng, Australian Open runner-up in 2024, raised her game to level the match but could not carry the momentum into the deciding set and slumped to her third successive first-round defeat at Wimbledon.
Siniakova's victory meant she avoided three successive Wimbledon first-round losses and she will face Japan's four-times major winner Naomi Osaka in the second round.
Earlier, American Jessica Pegula, the third seed, was dismantled 6-2 6-3 by Italian Elisabetta Cocciaretto.