The airline, which operates daily flights to Shanghai and Beijing from Heathrow, said it was halting the flights with immediate effect after the Foreign Office warned against "all but essential travel" to the country because of the virus outbreak.
A British teacher in Wuhan city, who said UK citizens were being given details of forthcoming flights, said flights taking Britons back home could begin as early as Thursday.
The deadline for those stuck in the city of Wuhan and surrounding areas to contact the British consulate expressing their wish to leave passed at 3am UK time (11am local time).
In a statement on Wednesday morning, British Airways said: "We have suspended all flights to and from mainland China with immediate effect following advice from the Foreign Office against all but essential travel.
"We apologise to customers for the inconvenience, but the safety of our customers and crew is always our priority.
"Customers due to travel to or from China in the coming days can find more information on ba.com."
It comes after the Foreign Office updated its advice on Tuesday to warn against "all but essential travel" to mainland China, saying it may become more difficult for British nationals in other provinces to leave.
The death toll in the country has risen to 132, with confirmed infections surging to nearly 6,000.
Four cases have been confirmed in Germany, making it the second European country to report cases, after France.
The United Arab Emirates has also confirmed its first cases of the virus in a family who recently returned to the UAE from Wuhan.
In Australia, officials unveiled plans to evacuate some of its nationals from Wuhan and the surrounding Hubei province, with plans to quarantine them in the Christmas Island immigration detention centre for up to 14 days - the incubation period for the virus.
In the UK, people coming back will be told to "self-isolate" and stay indoors for 14 days, but there are no plans to forcibly quarantine them.
The Department of Health and Social Care said 97 people in the UK have been given the all-clear for the virus, although scientists predict it may have entered the country.
Foreign Secretary Dominic Raab said officials are "working urgently to finalise arrangements for an assisted departure from Hubei province for British nationals this week, and are in contact with people in Hubei to ensure they register their interest and that we can keep them updated".
He added: "Due to the increasing travel restrictions and the public health situation, we now advise against all but essential travel to China."
The Foreign Office has said UK nationals in China should "make decisions based on their own personal circumstances" over whether to leave other parts of the country.
The British embassy in Beijing has said transport to get UK citizens out "may happen quickly and with short notice".
China has imposed travel restrictions between its major cities, while the Ministry of Culture and Tourism has suspended all tour group companies' activities to prevent further virus spread.
The British teacher living in Wuhan, who asked not to be named, told the PA news agency that a number of other Britons she was in contact with had arranged to return home, with some scheduled on a flight at 7am on Thursday.
Officials estimate up to 200 citizens currently there will want to return to the UK.
Hubei province has been on lockdown for several days as China seeks to contain the illness, as have other parts of China.
Hong Kong also said on Tuesday that it would "temporarily" close some of its borders with mainland China and stop issuing travel permits to mainland Chinese tourists.
On Monday, Health Secretary Matt Hancock said officials could not be 100% certain the virus is not spread by people who are not displaying symptoms and spoke of self-isolation".
The move means more than 1,400 people who have returned from Wuhan since January 10 should isolate themselves for 14 days from the date of leaving China.
Following the latest Foreign Office travel advice, consumer group Which? said people with trips to China planned should be covered for cancellations by their travel insurance.
Adam French, from the organisation, said those already in the country should be entitled to be flown out or be compensated for any changes to their itinerary.