They say it would be nonsense to travel that far when a vaccination centre is open at the Robert Jones and Agnes Hunt Hospital just five minutes from the town.
Many over 80s from Oswestry have already had their first vaccination at the hospital's vaccination hub and praised the facility.
But this week the North Shropshire Primary Care Network announced it is running a new Covid-19 vaccination centre from Prees Medical Practice. Those behind the scheme say patients in eligible groups will receive their invitation to attend either by text message or phone call.
The network, includes Caxton Surgery, Cambrian Medical Practice and Plas Ffynon Medical Practice as well as Churchmere, which has a surgery in Ellesmere as well as Whitchurch.
Mrs Dot Basham, from St Martins, near Oswestry, who is in her 70s and will be in the fourth tranche of vaccinations said it was ridiculous.
"We have a perfectly good vaccination centre on our doorstep that by all accounts provides a brilliant service," she said.
"There is no public transport to Prees while we have buses go past the Orthopaedic Hospital. I know the council has said it will provide free transport, but sitting in a vehicle all the way to Prees when we have the Orthopaedic - it is just ridiculous."
Many people took to social media to query the news.
This brought a response from the hospital which said: "We have received a number of calls today from members of the public concerned that the Oswestry Vaccination Hub based on our hospital site is closed.
"We can assure people this is not the case. Anyone with an appointment at the hub should please attend as planned."