The storm made landfall in Ulsan, just north of Busan, South Korea’s second-largest city.
More than 300 flights from 10 airports were cancelled, with some train services suspended.
Thirty-two people were injured, including four who sustained cuts after the glass windows of an evacuation centre were blown in, according to Japanese broadcaster NHK.
Some eight million people in Japan had been asked to evacuate in the path of the storm.
The storm comes days after Maysak, one of the region’s strongest typhoons in years, slammed into the Korean peninsula and Japan last week.
How has South Korea been impacted?
High winds have already cut power to almost 5,000 households on the southern tip of the Korean peninsula, including the resort island of Jeju, says a Reuters report.
But a KMA official told Yonhap News that it was likely the typhoon would weaken as it passed by.
South Korea’s Korea Forest Service had earlier raised the landslide alert to its highest level.
Nearly 430,000 homes in the Kyushu region were without power as of 03:00 local time Monday (18:00 GMT Sunday), Japanese public broadcaster NHK reported.
Haishen has led to the closure of factories, schools and businesses across western Japan. Hundreds of flights and train services were also cancelled.
The Gulf Livestock 1 was carrying 43 crew members and 6,000 cows when it went missing on Wednesday. Three crew members were rescued, though one later died.