Philip Dunne told Parliament this week there were parts of his constituency where no one in the community over 80 had been vaccinated.
He called on Matt Hancock, Secretary of State for Health and Social Care, to prioritise areas like south west Shropshire for vaccine deliveries.
Mr Dunne said: "There are still some parts of the country where only care homes and NHS Frontline staff have been vaccinated. And in the South West Shropshire Primary Care Network, no one in the community over 80 has yet received a vaccine. None are expected until late next week.
"So can my Right Honourable Friend, look at prioritising deliveries for those areas where the highest priority groups have yet to receive the vaccinations, which they are being led to believe are now widely available?"
The Minister replied that 14,000 vaccine doses had been delivered to the over 80 age group in Shropshire and Telford & Wrekin.
"I will look into the specific question of the Primary Care Network that he raises, because I was not aware of that fact," said Mr Hancock. "And clearly Shropshire is vaccinating the over 80s, but I will look into this specifically.
"And it is true that right across the country the catch-up of areas if they are behind, is absolutely vital, because it is right that this is done fairly across the country. And so I will get back to him with the details about the individual case that he raises."
Following the debate Mr Dunne said that the roll-out had been going "fantastically well" in the eastern part of his constituency but not others.
The MP for Ludlow explained that Bridgnorth benefited from suitable premises with parking nearby and the capacity to store the Pfizer vaccine on the premises.
This meant it had been able to progress the roll-out of vaccines relatively smoothly, as had Shrewsbury.
In the western half of his constituency, however, GP practices such as in Church Stretton lacked the capacity to store large quantities of the Pfizer vaccine, which needs to be kept at between -60c and -80c prior to use.
This meant it might be more appropriate to use the Oxford vaccine instead which did not need to be stored at such cold temperatures.
"This is not like the flu jab," said Mr Dunne. "It is a mammoth logistical undertaking, the like of which the country has not seen before.
"We can't do everyone straight away but I think they are going to catch up."