According to the Daily Mail Rev Philip Fowles, who works for the St Monica Trust in Bristol as pastoral director, said he wanted Anna Soubry (above) to "burn in hell" because she supported a soft, rather than hard Brexit. He also used an expletive.
Rev Fowles is also one of the church leaders at Nailsea United Reformed Church.
The email, sent from a St Monica Trust account, said: "Madam, You are a traitor to the British people who have voted to leave the EU to build a better Britain outside of their sticky-fingered control.
"You are also a disgrace to our great party."
Anna Soubry's parliamentary staff reported the email to police and Rev Fowles has now apologised.
He said in an email the next day: "I write to offer our unreserved apology for the tone of our email communication to you.
"Unfortunately, the whole communication inadvertently went via the St Monica Trust website and whilst the views expressed were heartfelt and personal they in no way represent those of the Trust."
St Monica Trust has said it's suspended Rev Fowles and is running an internal investigation.
Anna Soubry told the Daily Mail: "This kind of hateful behaviour is appalling and has no place in a democracy."