But bosses have announced plans to try and keep the post office inside the shop in Anglesey Street open.
A consultation period began on Friday and will finish on January 10, and if the plans go ahead the store – which is less than half a mile away from a Tesco Superstore and an Aldi – will shut its doors for the final time on January 26.
A Midcounties Co-operative spokesman said: "The long-term viability of our Hednesford food store has been reviewed, and despite the hard work of our colleagues sales have fallen and continue on a downward trend, with the profitability of the store being impacted.
"As a result, the society has taken the difficult decision to propose to close the Hednesford food store.
"It is anticipated that if the closure proceeds, the store will close at the end of the financial year on January 26, 2020.
"The proposal is to continue to trade the post office as normal, and the society is considering the building design to allow that to happen once the food store has closed.
"The consultation period commenced on October 4, 2019 and is proposed to conclude on January 10, 2020."
Staff at the post office inside Hednesford Co-op, in Anglesey Street, have been told the business is proposing to close the food store next year.
A post office spokesman, said: “The operator for Hednesford post office has recently announced to staff that they are proposing to close the food store next year.
"We have not yet received a resignation.”
But the chairman of Hednesford Town Council, Councillor Paul Woodhead, said the decision could "devastate" the town.
He said: "It is extremely worrying that another business in our town is considering its future and commitment to our community.
"As a Co-operative we hope they consider their values towards community and remain a key part of our town and we appeal to Midcounties Co-operative to talk to us before making a decision which could devastate our town and further undermine the fragile high street economy.
"We need investment not desertion."