Two members had already set out on their journey – one has now turned back and the other is in transit in a third country, the BBC reported on Wednesday.
The WHO said the problem was a lack of visa clearances.
The long-awaited probe was agreed upon by Beijing in December after many months of negotiations with the WHO.
The virus was first detected in Wuhan in late 2019, with the initial outbreak linked to a market.
WHO chief Tedros Adhanom Ghebreyesus said he was “very disappointed” that China had not yet finalised the permissions for the team’s arrivals “given that two members had already begun their journeys and others were not able to travel at the last minute”.
“I have been assured that China is speeding up the internal procedure for the earliest possible deployment,” he told reporters in Geneva on Tuesday, explaining that he had been in contact with senior Chinese officials to stress “that the mission is a priority for WHO and the international team”.
The WHO has been working to send a 10-member team of international experts to China for months with the aim of probing the animal origin of the pandemic and exactly how the virus first crossed over to humans.
Last month it was announced that the investigation would begin in January 2021.
The two members of the international team that had already departed for China had set off early on Tuesday, said the WHO.
WHO emergencies chief Mike Ryan said one had turned back and one was in a third country.
Covid-19 was first detected in the Chinese city of Wuhan in central Hubei province in late 2019.
It was initially believed the virus originated in a market selling exotic animals for meat. It was suggested that this was where the virus made the leap from animals to humans.
But the origins of the virus remain deeply contested. Some experts now believe the market may not have been the origin, and that it was instead only amplified there.
Some research has suggested that coronaviruses capable of infecting humans may have been circulating undetected in bats for decades. It is not known, however, what intermediate animal host transmitted the virus between bats and humans.