The Times report, published Thursday in both English and Chinese, said Wen's relatives "have controlled assets worth at least $2.7 billion."
"Many relatives of Wen Jiabao, including his son, daughter, younger brother and brother-in-law, have become extraordinarily wealthy during his leadership," the newspaper said.
"In many cases, the names of the relatives have been hidden behind layers of partnerships and investment vehicles involving friends, work colleagues and business partners."
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In addition to blocking the Times website, Chinese censors have also blocked references to the report on micro-blogging sites such as Sina Weibo.
Searches for "New York Times" and "NYT" in Chinese returned a message that the result could not be displayed "due to relevant laws," Agence France-Presse said.
When asked about the story, a Chinese foreign ministry spokesman said it had "ulterior motives."
"Some reports smear China and have ulterior motives," spokesman Hong Lei told reporters during a daily press briefing in Beijing, according to AFP.
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The Times report comes during a time of heightened sensitivities in Beijing, with China's Communist Party preparing for a once-a-decade leadership transition.
Nicknamed "Grandpa Wen" for his folksy public persona, the Chinese premier is due to step down during the change in leadership.
Bloomberg's website is still blocked in China after the news agency in June published a similar investigation into the finances of Xi Jinping.
Xi is widely expected to succeed Hu Jintao as the country's next president.
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