A restriction zone has been set up around the farm and culling has begun, said a spokeswoman for the Department for Environment, Food and Rural Affairs.
"We have confirmed a case of avian flu on a duck breeding farm in Yorkshire," the spokeswoman said.
"The public health risk is very low and there is no risk to the food chain," she said.
Avian influenza is fatal for chickens, and poses a health threat to humans, who can become sickened by handling infected poultry.
The H5N1 strain of bird flu has killed more than 400 people, mainly in Southeast Asia, since first appearing in 2003. Another strain of bird flu, H7N9, has claimed more than 170 lives since emerging in 2013.
The British official did not specify which exact strain was detected at the farm in Yorkshire.
Dutch officials earlier on Sunday banned the transport of poultry in the Netherlands after the discovery of a highly infectious strain of bird flu which could jump to humans.
The "highly pathogenic" form of avian influenza discovered at a farm in the centre of the country is very dangerous to birds and "contamination can occur from animals to humans," the Dutch government said in a statement.