The storm lashed "Hainan with heavy rain and gusty winds, leaving at least two dead and 92 injured", state-run news agency Xinhua said, citing local authorities.
State broadcaster CCTV said Yagi brought winds of more than 230 kilometres (143 miles) per hour, uprooting trees and prompting the evacuation of around 460,000 people on the island.
The storm made landfall Friday on Hainan, a popular holiday destination.
The island's main airport in Haikou was closed until 3 pm on Saturday (0700 GMT), according to state broadcaster CCTV.
Authorities in the neighbouring province of Guangdong said on Friday that they had evacuated more than 574,000 residents to safety.
Yagi killed at least 13 people in the Philippines earlier this week, when it was still classified as a tropical storm, before strengthening into a super typhoon over the next few days.
The storm will head towards Vietnam after moving through southern China, on course to hit the northern and north-central regions around the famed UNESCO heritage site Halong Bay on Saturday.
News » International
Super Typhoon Yagi kills 2, injures 92 in China: state media
Super Typhoon Yagi killed at least two people and injured 92 others after slamming into southern China's Hainan island, state media reported Saturday.
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