Shropshire Council has issued the warning as it makes plans for how to deal with the situation – with current estimates saying the shortfall could be between £2.5m and £9.7m.
The authority has said that the issues caused by the pandemic, as well Brexit implications, make it "harder than usual" to predict what its end of year budget position will be.
A report on the situation will be discussed by the council's cabinet on Wednesday.
Despite the potential range from £2.5m to £9.7m the report suggests the council is likely to face a £7.3m budget shortfall "if no action is taken".
Gwilym Butler, Shropshire Council’s Cabinet member for resources has said that the council is now looking at ways to address the gap.
He said: "We face a unique set of challenges created by the pandemic, pressures such as social worker shortages for vulnerable children, and supply chain issues that are affecting many parts of the economy.
"The first report of the year covers a period entirely impacted by pandemic restrictions, making the job of projecting our financial position even harder, but it’s very important that we plan and prepare now for the uncertainties.
"This includes making sure that our activity aligns with our objectives and plans for a healthy economy and a healthy population for Shropshire, and that all we do is best value using our resources in the best way we can.
"The most worrying concern is our longer-term deficit. This shows why we must continue to fight for fairer funding, and against a system that ignores the extra costs we must meet to provide services in one of England’s most sparsely populated and rural counties.
"In Shropshire it costs us more, for example, to provide social care over sparsely populated distances. We have one of the biggest road networks to maintain in England, yet receive lower funding per mile than many other councils."
Among the key reasons for the projected shortfall is the continuing pressure on children’s safeguarding services and loss of income for services such as schools catering, car parking and commercial property income, all of which have been directly impacted by the pandemic, and a delay in the council’s transformation programme.
However, more grant funding could yet be announced by the Government, particularly to help with one-off pressures linked to the pandemic – although the authority says it cannot rely on this coming forward, and must therefore plan accordingly.
A statement from the council said: "Finance teams are also working with services to identify how they can meet the shortfall and many mitigating actions are being developed, which will help address the in-year challenge as well as the longer-term underlying budget deficit of c£39 million rising to £58 million by 2025/26, much of which has been hidden by one-off grants and Government funding in recent years."