Norrie had played just one match on grass before this year's Wimbledon after retiring injured in the French Open first round with a rib injury.
And the former world number eight looked rusty as he broke Zheng, ranked 144th, just once in the entire match.
Zheng hit 21 aces to Norrie's four, while the 22-year-old committed just four double faults to Norrie's 10.
Harriet Dart came close to completing a gritty comeback win but ultimately fell 6-3 3-6 6-4 to former French Open champion Jelena Ostapenko.
The pair were scheduled to play on Court 17 on Monday, but Raducanu's withdrawal saw their match moved to Court One.
Wildcard Dart made sure that fans with tickets for the show court were not disappointed as she forced a deciding set against the world number 31 in an entertaining two-and-a-half hour display.
Ostapenko will face either Antonia Ruzic of Croatia or compatriot Darja Semenistaja - the lucky loser who replaced Raducanu in the draw.
Meanwhile, 17-year-old British wildcard Mika Stojsavljevic lost 6-2 6-1 to 2021 Olympic champion and 11th seed Belinda Bencic.
Felix Gill and Max Basing were beaten on their Grand Slam main-draw debuts, losing to 23rd seed Rafael Jodar and qualifier Shintaro Mochizuki respectively.
Alicia Dudeney, who was also making her main-draw major bow, lost 6-3 6-3 to American Alycia Parks.
It means home hopes on the opening day's play rest on teenager Hannah Klugman, Mimi Xu, Francesca Jones, Oliver Tarvet and Jack Pinnington Jones.
There are 19 home players across the two singles draws - although 17 are playing opponents ranked inside the world's top 55.