The service, for the South Shropshire hunt, The United Pack, had been due to take place at St George’s Church in Clun on Sunday.
But the Diocese of Hereford, which is responsible for the church, said it had decided to cancel the service after comments about a member of the clergy on the internet.
In a statement, the diocese said that a member of the church had been the subject of “a number of untruths spread online”.
It added: “Based on police advice, we have taken the decision that the service will not go ahead. There have been a number of untruths spread online about a member of our clergy who it was assumed would be leading this service. The decision has been made in the interests of her personal safety.
"Our churches remain open to everyone and offer anyone a welcome, whatever their belief or world view.”
Threats came after a Facebook post asked people to e-mail their thoughts to a reverend, and to “keep it polite”.
A spokesman for The United Pack said new arrangements were being made, blaming a “hate-filled campaign against local clergy” on social media.