They broke out around 04:00 on Saturday (20:00 GMT Friday) at one of the country's largest refining and petrochemical plants.
Flames could be seen engulfing parts of the sprawling complex and spewing thick columns of black smoke into the sky.
Shanghai is China's economic hub and only recently emerged from a strict pandemic lockdown lasting two months.
The cause of the fires, which affected an ethylene glycol facility, is still unclear.
