The game has roughly 55 million daily active users and analysts estimate its monthly revenue is more than 1 billion yuan ($147.09 million), making it the firm's top-grossing game.
It comes as Tencent announced this week it would slash the number of hours underage users can access the app, amid a wider campaign by the Chinese authorities to stamp out gaming behavior that it deems "harmful to the psychology of minors".
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The new bans restrict players under 12 to one hour of game play a day and limits users under 18 years to two hours.
China's People's Daily called the game "poison", alluding to a Chinese gaming term used to describe addictive games and called for the industry to be further regulated.
Tencent stock has dipped by 4.2 per cent since the bans were announced on Monday.
The multi-player role playing game is free, but allows users to purchase items to advance more quickly in the game.
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The game's launch in the Europe Union and the United States marks its first attempt to bring the massively popular homegrown franchise to western markets.
Tencent has previously acquired top-grossing foreign titles, including an $8.6 billion majority stake in "Clash of Clans" maker Supercell, but it is yet to export self-produced games of the same size to Western markets.
A Tencent spokeswoman said it currently had no timeline for the game's expansion.
Honour of Kings is already available in markets in Asia including Taipei, Thailand and Hong Kong, as well as Turkey.
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