The artwork, which shows events leading up to and including the Battle of Hastings in 1066, is being insured for £800m by the Treasury.
But Hockney said that figure was “meaningless”, insisting: “It is priceless.”
He said transporting it for the exhibition involves “significant risk”.
“The linen backing is weakened by age, and the wool embroidery threads are vulnerable to stress,” he said, adding that he had researched the process.
“Rolling, unrolling or handling it in a new way can cause damage.”
He noted it had been kept safe “for centuries” in Bayeux, where it is kept in “tightly-controlled conditions”.
The artwork has already been taken off display and moved into storage in preparation for its journey to London.
Hockney claimed the move was being carried out for “the vanity of a museum which wants to boast of the number of visitors”.
The British Museum said it was working closely with conservators and specialists in France before transporting the tapestry.
Cullinan said they “send and receive thousands of loans each year – including ancient frescoes and textiles which are older than the Bayeux tapestry”.
He added that their condition and safety was “always of paramount importance”.
The tapestry tells the story of the Norman conquest of England in 1066 and is widely believed to have been created in Kent.
It is made up of 58 scenes, 626 characters and 202 horses, and depicts William the Conqueror taking the English throne from Harold Godwinson, becoming the first Norman king of England.
In exchange, British treasures including artefacts from Anglo-Saxon burial mounds at Sutton Hoo and 12th Century Lewis chess pieces are being loaned to museums in Normandy.