Thousands of ducks are being culled after a case was detected at a poultry farm in East Yorkshire.
A six mile restriction zone is in place around the farm but the government says the risk to humans is very low.
Bishop of Selby Rt Revd John Thomson told Premier the Church was working hard to help locals.
He said: "We express our pastoral concern for people facing such a traumatic reality.
"I've already been in contact with the local vicar and he is looking to find ways of expressing that support to local people.
"Our message is that we have registered it, local people are aware and are doing what they can on the ground.
"They are in our prayers."
Chief veterinary officer Nigel Gibbens said this might not be the last case we see.
He told the BBC: "We cannot rule out that there might be further cases; this is why we put premises under restriction to look for further spread.
"Because there's a wild bird risk we also need farmers and their vets all over the country to be alert to possible disease in their farm that they can't explain, draw those to our attention so we can investigate quickly, and, if there is any more disease, seek to nip that in the bud as well."
The last major case of bird flu in the UK was in 2008 in Banbury, Oxfordshire.
The Department for Environment, Food & Rural Affairs (Defra) insisted the risk to public health is "very low" and there is no risk to the food chain.