It is the fourth cancellation in a week.
Foreign ministry officials said last week that Mr Xi would meet the Danish prime minister, but now deny the meeting was ever scheduled.
Mr Xi is expected to be appointed China's new leader at the Communist party congress next month.
No explanation has been given for his failure to meet the American Secretary of State, Hillary Clinton, and delegations from Russia and Singapore last week.
The latest cancellation followed a frenzy of speculation about Mr Xi's health on Chinese-language websites based overseas, one of which said that he had been involved in a car crash - a report it later retracted.
The site, Boxun, blamed the error on "leftists . . . trying to create rumours" and said that Xi in fact had only some minor health problems. Other overseas media reported that he was suffering from back problems.
In an indication of the sensitivity surrounding the issue, Danish embassy spokesman Ming Ou Lu refused to confirm or deny that a meeting between the two had even been scheduled.
China's foreign ministry spokesman Hong Lei also evaded repeated questions about Mr Xi's absence at a daily briefing for foreign media on Monday, saying that he had "no information" to provide.
"Obviously the Chinese authorities are also concerned about any news that may create an adverse speculation concerning the leadership succession process," said Joseph Cheng, China scholar at Hong Kong's City University.
"They are so worried and sensitive. (The result is) that they have not been acting sensibly."