The vaccination programme for 12 to 15 year olds in the county began last month, and the team in charge of the operation say the aim is to have "most children" being offered the vaccine in a session at their school "before December".
It means county schools should all have had the chance to host a Covid clinic before Friday, October 22.
Although no figures are yet available for the number of children to have received the jab, a spokeswoman for the Shropshire, Telford and Wrekin Covid-19 Vaccination Programme said the response from children and parents had been "very positive".
In Mid Wales all children aged 12 to 15 will also be offered a Covid vaccination "by the October half term", according to the Welsh Government.
It comes as there have been protests outside some county schools over the issue, while Shropshire and Telford & Wrekin schools were also targeted with 'fake NHS' surveys by anti-vaxxers.
The spokeswoman for the county's vaccination programme said: "The Shropshire, Telford and Wrekin Covid-19 Service in conjunction with the School-Aged Immunisation Team have started vaccinating 12 to 15 year olds in schools.
"The aim is to have offered all schools the opportunity to have a Covid-19 Clinic by half-term with most children having the vaccine in a session at their school before December.
"The overall response from parents and children in schools has been very positive."