Schools, offices and the stock market in the northern part of the island were ordered closed to guard against damage or injuries as the storm swept past Taiwan.
Flights from Taiwan to Japan, South Korea and a few other Asian countries were cancelled, officials said.
Whipping up waves up to 10m high, Wipha was moving northwest across the sea north of Taiwan at about 25kph, weather reports said.
Wipha was upgraded from a tropical storm on Monday afternoon, and local meteorological officials said it was likely to build in strength as it moved across the sea toward Shanghai.
Packing gusts of up to 300kph, it could be the most destructive storm to hit the Shanghai area – home to more than 14 million people - in years.
Officials said those ordered to evacuate include residents of old and dangerous houses, workers who live in temporary construction site structures as well as workers living near the shore.
The heavily populated provinces of Zhejiang and Fujian next to Shanghai are also on high alert
"The typhoon is very likely to develop into the worst one in recent years. We are still observing it. It's hard to say at this moment," said an official at Shanghai's meteorological bureau.
After lashing Shanghai, the typhoon is expected to head out to sea again towards the Korean peninsula, where another typhoon, Nari, left at least 20 people dead or missing over the weekend, local media reported.
Nari pounded South Korea's southernmost Jeju island and southwestern regions on Sunday with heavy rain and gusts of up to 150kph.