Twenty-five crew members went to local hospitals as a precaution but were later discharged, said BA spokeswoman Michele Kropf.
The crew were not treated for smoke inhalation as reported, she said.
The airline did not say what the cause of the problem was or what their symptoms were.
There has been no confirmation over how many people the Airbus A380 carried.
Images showed emergency vehicles surrounding the plane on the tarmac.
The flight BA286 departed at 19:13 on Monday (02:13 GMT) and landed in the Canadian city several hours later.
BA said passengers had been put up in hotels and would be rebooked on other flights.
Gavin Wilson, public affairs director for Vancouver Coastal Health, said all 25 crew members have been released as of 5am local time (12:00 GMT)
"They were brought into hospital as a precaution and they were subsequently discharged early this morning," he told the BBC.
Various crew members were sent to three separate Vancouver-area medical centres: Vancouver General Hospital, Delta Hospital and Richmond Hospital.
At the moment there are no further details on the reason for their hospitalisation.
"I can't tell you at this point what they were assessed for," Mr Wilson said.
A British Airways flight from San Francisco to London was diverted to Vancouver after members of the crew became ill, the airline says.