Councillor Drew Tarmey said the next closest branch was at the other end of the town centre.
“Rotherham is a flagship post office located right in the town centre next to public transport links at the train and bus stations.
“It is really important for people who are not confident using online services.
“Post offices are even more important now we are seeing banks close their Rotherham branches, they are going to become banking hubs in the future.”
He added: “People used to go to a local branch of their bank but when they closed down, they started going to the post office to withdraw and deposit cash to their accounts.”
The Post Office has launched a new five-year plan and said it was considering a range of initiatives to “boost revenue, drive efficiency and reduce costs”.
A spokesman said: “As part of this process, we are considering the future of our directly managed branches, which are loss-making. However, no decisions have been made.
“We are inviting expressions of interest to operate post offices, including Rotherham, to gauge market interest and explore whether franchising could be a viable option.
“We will review all responses, sharing the results with relevant trade unions and other stakeholders.”
The Liberal Democrat group of councillors have asked Rotherham Council to formally oppose the potential closure.
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