The MSN & Lunts Pharmacy group has been commissioned by NHS England to provide the service.
Helen Whitehouse, operations manager for MSN & Lunts Pharmacy group, said: "We have been running a successful Covid clinic at our pharmacy branch in Great Bridge since the beginning of June therefore we are well equipped and experienced in this field.
"Delivering primarily booster vaccinations we are also able to deliver first, second and third doses.
"The demand has been through the roof as many local people in the area have not been in a position to travel to get their vaccines.
"The original proposal was to deliver 350 vaccines per week in branch.
"Over this last weekend we have delivered over 1,000 vaccines across the three branches with clinics running into the evening."
In addition to the two new sites, its pharmacy in Highley, near Bridgnorth, is also due to start the service within the next few weeks.
Pontesbury pharmacy has also just had a major refit with a new larger well equipped consultation room, which bosses say has been met with approval by all of the customers.
Ms Whitehouse added: "Craven Arms pharmacy serves a large community and surrounding villages and NHS England has now approached us further to increase the delivery in Craven Arms to exceed the original 350 as we are the only pharmacy within south Shropshire providing the vaccines.
"We are confident we can increase delivery in this service and look forward to the challenge."
Appointments can be made via the national booking service at nhs.uk/conditions/coronavirus-covid-19/coronavirus-vaccination/book-coronavirus-vaccination.