A journalist and stock market officials are among those arrested, Xinhua said. It gave no other details.
Chinese shares fell by nearly 8% after a week of volatile trading that spread fear to global markets.
The Tianjin explosions killed 150 people – with 23 still missing.
A total of 367 people remain in hospital after the August 12 blast at a Tianjin warehouse where large amounts of toxic chemicals were stored. Twenty are in critical condition, according to Xinhua.
Separately, the UK’s Financial Times says Chinese leaders feel they mishandled their stock market rescue efforts.
The publication, quoting an account of a meeting of senior regulatory officials on August 27, said the government had decided to abandon attempts to boost the stock market and instead step up efforts to punish people suspected of “destabilizing the market”.
Chinese authorities tightly control information online and have previously prosecuted internet users for spreading rumors.
The rumors described by the latest statement include reports that a man had jumped to his death in Beijing due to the stock market slump and that as many as 1,300 people were killed in Tianjin blasts, Xinhua said.
The news agency said “seditious rumors about China’s upcoming commemorations of the 70th anniversary of the end of World War II” were also among the offences.
A journalist was also arrested along with several stock market officials, according to a Xinhua report. The journalist, Wang Xiaolu, is accused of “spreading fake information” about the market slump, the report said.
Xinhua said Wang Xiaolu confessed that he “wrote fake report on Chinese stock market based on hearsay and his own subjective guesses without conducting due verifications”.
In 2013 China introduced a possible three-year sentence for spreading rumors – the sentence was supposed to apply to anyone who posted a rumor that was reposted 500 times or viewed 5,000 times.
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