"It is forbidden for websites to carry out live streaming or picture reports of the inauguration," the Financial Times reported.
Online media outlets were also reminded to "take care of news comments... and negative and harmful speech", according to the report.
Most media yesterday reported only briefly on Mr Trump's swearing-in ceremony, using reports from the state-run Xinhua news agency. One leading newspaper even reduced its planned four-page coverage to just one story laying out Mr Trump's domestic economic policy.
Similar orders are common for major world events but analysts said that in this case, it reflected uncertainty in Beijing over how to handle public perceptions of Mr Trump, according to the Financial Times.
"The government is still working out how to react to him, which is why in this case they are taking very close control of the media for this event," a Beijing Foreign Studies University professor of international journalism, Dr Zhan Jiang, was quoted as saying.
In a recent interview with the Wall Street Journal , Mr Trump said the "one China" policy was up for negotiation. Beijing, however, considers the policy the non-negotiable foundation of bilateral ties.
Mr Trump also broke with decades of precedent last month by taking a congratulatory telephone call from Taiwanese President Tsai Ing-wen, angering Beijing, which sees Taiwan as part of China.
A Xinhua commentary in English yesterday downplayed potential confrontation, saying both nations now enjoyed "more room for cooperation than ever before" in dealing with unconventional global security challenges such as terrorism, global warming and cyber security.
"The world expects him to deal with the US and global challenges with discretion and wisdom, and give full play to China-US cooperation to conquer the hardships," said the commentary.
A version of this article appeared in the print edition of The Sunday Times on January 22, 2017, with the headline 'Chinese news media plays down coverage'.