SHANGHAI—Electric-car maker Tesla Inc. says it has hit its early production target of 1,000 vehicles a week at its China plant, less than a year after breaking ground at a 210-acre field in Shanghai.

Song Gang, who oversees the production at the factory, said Monday that Tesla can now produce 28 vehicles or more an hour and has implemented a 10-hour workday. Mr. Song spoke at an event where 15 of Tesla’s first made-in-China Model 3 sedans were delivered to customers, all Tesla employees. The company is set to start larger-scale delivery next month, another executive said.

The success of the Chinese plant—known as Gigafactory Shanghai—is crucial for the Silicon Valley-based car maker led by Elon Musk, who is betting big on the world’s biggest automotive market. Tesla grappled with Model 3 production at its Fremont, Calif., plant after the car was launched in 2017.

“We can’t show you every detail of our hard work. But what we can show is the result,” Tesla Global Vice President Tao Lin said at Monday’s event. “Every made-in-China Model 3 running on the street proves our daily efforts are worthwhile.”

Producing cars locally for the Chinese market allows Tesla to cut back on shipping costs and avoid import duties. In April, Mr. Musk said Tesla’s production in China could hit 1,000 to 2,000 vehicles a week.