The Telford International Centre, capable of delivering up to 10,000 vaccinations a day, is either not operating, or delivering nowhere near capacity, Telford & Wrekin Council leader Shaun Davies has said.
It it also understood that other mass vaccination sites at Ludlow and Shrewsbury Indoor Bowling Centre, are operating on an extremely reduced basis until vaccine supplies increase.
Because of national shortages in the supply of vaccine the government has prioritised the remaining people over 50, who have not yet had the jab, and second doses.
Both Shropshire and Telford & Wrekin have given the vast majority of the eligible population their first dose vaccine – 98 per cent in Telford & Wrekin and 94 per cent in Shropshire.
It means Shropshire's centres have very few people left to deliver vaccinations to, resulting in the centres being effectively temporarily mothballed until supplies increase and the criteria is extended.
NHS Shropshire, Telford and Wrekin CCG, which runs the county's vaccine operation, has declined to confirm which sites are currently working, saying only that "some of our sites may be operating at slightly different times".
It is understood that the Telford, Ludlow and Shrewsbury sites will reopen to deliver second doses later this month.
Some training sessions have also been taking place for volunteers at the sites.
Councillor Davies said that the success of the vaccination programme so far had led to a situation where the county was being punished for its progress.
He said: "It is clear that for the last two weeks the TIC has not been operating, either at all, or anywhere near capacity. It is really important the government and the NHS are clear as to the reasons why.
"We should also not be punished by the national decision makers for doing so well. We should be allowed to move to the under 50s."
Claire Skidmore, interim accountable officer for NHS Shropshire, Telford and Wrekin CCG, said vaccines are still available to those eligible.
“Over the coming weeks some of our sites may be operating at slightly different times due to the anticipated national decrease in vaccine supply," she said.
"Despite this, we will continue to offer the first dose of the vaccine to those who are eligible as well as administering second doses.”
The situation in Shropshire contrasts with that over the border in Powys, where the health board has opened up two short-notice reserve lists allowing people from 40-49 and from 30-39 to sign up for slots when they become available.
Those signing up are asked whether they would be able to make it to one of Powys's two mass vaccination sites with 30 minutes notice.