The Times said its employees have faced challenges securing work permits and it would move its digital team of journalists, roughly a third of its Hong Kong staff, to the South Korean capital over the next year.
The move delivers a blow to the city's status as a hub for journalism in Asia, and comes as China and the United States have clashed over journalists working in each other's countries. Earlier this year, Beijing said journalists no longer allowed to work in mainland China could not work in Hong Kong either.
"Given the uncertainty of the moment, we are making plans to geographically diversify our editing staff," a spokeswoman for The Times told Reuters.
"We will maintain a large presence in Hong Kong and have every intention of maintaining our coverage of Hong Kong and China."
Hong Kong returned from British to Chinese rule in 1997 with the promise of a high degree of autonomy, which has preserved the city's tradition of a freewheeling press and allowed international media to use it as their Asia hub.
The new national security law, which punishes what China broadly defines as secession, subversion, terrorism and collusion with foreign forces with up to life in prison, has stoked worries about freedom of speech and that of the media.
Authorities insist those freedoms remain intact but say national security is a red line.
Hong Kong leader Carrie Lam has said reporters can report freely in the city if they do not violate the security law. Her office did not immediately respond to a request for comment.
Earlier this year, Washington began treating five major Chinese state-run media entities the same as foreign embassies, then slashed the number of journalists allowed to work for Chinese state media to 100 from 160, previously.
In retaliation, China said it was revoking the accreditations of American correspondents with the New York Times, News Corp's Wall Street Journal and the Washington Post whose credentials expire by the end of 2020.
Beijing has also expelled three Wall Street Journal correspondents - two Americans and an Australian - following an opinion column by the newspaper that called China the "real sick man of Asia."