Dereham's Post Office branch is under threat of closure as part of a major effort within the organisation to reduce costs.
The Post Office has announced a five-year plan to deliver "a new deal" for its postmasters.
As part of its plans, the organisation is "considering the future" of its directly managed branches that are losing money as the Post Office moves to become a fully franchised network.
READ MORE: Where can you share your views on Breckland's car parking charges?
Post Office said it is considering "a range of options" to reduce its central costs.
Dereham's post office on Quebec Road is the only directly-managed branch in the NR postcode and is on the "hit list" of possible closures.
Dereham councillors, Harry Clarke and Ray O'Callaghan, were shocked at the news.
Mr Clarke said: "We are dismayed and shocked at hearing the news today. We really don't need this.
READ MORE: Dozens attend meeting to try and save town surgery
"There has always been a Post Office in Dereham. Like other market towns and villages, the Post Office is part of the glue that holds our social fabric together."
Mr O'Callaghan, who is also the town's deputy mayor, agreed.
He said: "Sadly, the last decade has seen the public realm and facilities and services diminish or face closures.
"We very much hope that any closure is avoided and that at least a franchise steps up. We will support any efforts to keep this service going."
READ MORE: Mother of three brings back Christmas joy for another year
Mid Norfolk's MP George Freeman said: "The importance of the service our local branches provide in a rural area like ours cannot be overstated.
"I will be speaking with the Post Office as a matter of urgency to highlight why this branch is a necessity for the people of Dereham."
A spokesman for the Post Office said: "We are considering a range of options to reduce our central costs.
"This includes considering the future of our remaining directly managed branches, which are loss-making.
"We have long held a publicly-stated ambition to move to a fully franchised network and we are in dialogue with the unions about future options for the DMBs."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here