Beijing successfully lobbied for the removal of a third of the report, entitled the "Cost of pollution in China" arguing the contents could lead to social unrest, the London-based newspaper said.
China's State Environment Protection Agency (SEPA) and health ministry asked the World Bank remove the figures from a draft of the report finished last year that stated about 750,000 people die prematurely each year from pollution.
China also successfully pushed for the removal of a detailed map showing which parts of the country suffered the most deaths, the newspaper said.
"The World Bank was told that it could not publish this information. It was too sensitive and could cause social unrest," the Financial Times quoted one adviser to the study as saying.
The draft was released at a conference on sustainable development in Beijing in March, and remains available on the Internet, without the sensitive data.
The World Bank, which put together the report in cooperation with Chinese government ministries over several years, acknowledged on Tuesday that some data had been withdrawn from the draft but did not go into details.
The World Bank said in a statement sent to AFP that the published version "did not include some of the issues that are still under discussion."
The statement said the final report was "still under review," while there was no comment on the allegations that Chinese pressure had led to the sensitive data being removed.
The published report on the Internet said "conservative" estimates put the cost of premature death caused by air pollution in China at 157.3 billion yuan (20.7 billion dollars) in 2003, but gave no estimates on the numbers affected.
Its foreword said that "certain physical impact estimations" had been left out of the draft of the report "due to... some uncertainties about calculation methods and its application."
Guo Xiaomin, a retired SEPA official who coordinated the Chinese research team, told the Financial Times the cuts were made partly because of concerns that the methodology was unreliable.
But he added the information on premature deaths "could cause misunderstanding," the newspaper said. Guo also expressed concerns over the size of the 148-page report.
"We did not announce these figures. We did not want to make this report too thick," he told the Financial Times.
Officials from China's environment agency or health ministry were not available for comment on Tuesday, while the foreign ministry refused to comment.
China's communist rulers have a history of suppressing information that they perceive as sensitive. However, in recent years they have pledged to be more transparent.
In 2003, the deadly SARS virus originated in China the government was widely condemned for initially covering up the disease, enabling the virus to spread around the world more easily.
Foreign media, informed by a retired army whistle-blower doctor Jiang Yanyong, eventually exposed the cover-up, but the disease went on to kill over 800 people worldwide, including 349 in China.
Despite the pledges of transparency, the government-controlled press continues today to ignore or play down sensitive issues such as protests and environmental accidents.