The report said most of Wen's family's wealth was accumulated after he rose to high office in 2002.
Chinese censors also blocked the Times' Chinese-language site that carried a translated version of the story.
Chinese Foreign Ministry spokesman Hong Lei told reporters at a press briefing that the report "blackens China and has ulterior motives." He refused to elaborate despite several follow-up questions.
Times' spokeswoman Eileen Murphy says the paper hoped access to the sites could be restored shortly.
While Wen is expected to leave his post in the spring, the report is a blow to his reputation as a politician concerned with bettering the lives of ordinary Chinese.