Mark Pritchard, MP for The Wrekin, was also given an assurance that all his constituents who had been invited to receive the injection at the main vaccination centres in Birmingham and Manchester would shortly be offered the jabs at a site in the county if they found the journey too far.
Mr Pritchard said some of his constituents had received letters inviting them to to attend vaccination centres up to an hour and 45 minutes away.
But health minister Nadhim Zahawi assured him that all his constituents eligible for the jab would be able to receive the injection at a time and place convenient to themselves.
"I absolutely join my honourable friend in congratulating and thanking the heroes of the NHS and the volunteers in Telford and Wrekin and Shropshire for vaccinating 15,000 of the most vulnerable people to Covid who, in a couple of weeks’ time, will have that protection," said Mr Zahawi.
"He is right, I can confirm, that anyone receiving a letter where it is inappropriate or not possible for them to travel that distance to a national vaccination centre does not have to do so.
"They will be able to be vaccinated in their primary care network at a time and place that is convenient to them."