More than 600 flights from the city's two airports were canceled and high-speed rail services also impacted, said state broadcaster CCTV.
The typhoon first hit the island of Chongming, 45 km (28 miles) east of the city, with winds of up to 28 meters per second (62 miles per hour) near its eye, said the National Meteorological Centre, Reuters reported.
The city had already relocated 190,000 people from coastal areas by early Sunday morning, said a report by state news agency Xinhua.
Shanghai Disney Resort said it was operating as normal but some outdoor attractions and performances would be suspended during periods of heavy rain or high winds.
Shanghai Tower, the tallest building in China, has suspended rooftop sightseeing, according to Xinhua.
In neighboring Zhejiang and Jiangsu provinces, more than 42,500 people were relocated. More than 28,000 ships including 22,900 fishing boats have returned to port in Zhejiang, added the report.
Heavy rain and thunderstorms in recent weeks have caused havoc across China, with floods along major rivers destroying bridges, blocking roads and railways and forcing thousands of residents to evacuate.