The funding forms part of additional £150 million to expand and upgrade 25 A&E facilities in hospitals across England.
This is meant to ensure they have improved physical space to treat patients, manage patient flow and improve infection control.
A £2 million boost was announced last month for Princess Royal Hospital in Telford.
Mr Dunne said: “I am very pleased SaTH will receive an additional £6.3 million to help prepare the A&E at the Royal Shrewsbury Hospital for the winter ahead.
"This is part of £450m to upgrade A&Es across England.
“I also welcome the NHS putting £24 million into pilots to increase 111 call handling capacity, with more clinicians on hand to provide expert advice and guidance.
"NHS 111 has handled millions of calls during the pandemic, and this investment will ensure the call handlers can book appointments for patients with the appropriate service to cut out unnecessary queueing and ensure they get the right care first time.”
To ensure patients get the right care in the right place and avoid unnecessary visits to emergency departments, NHS 111 will build on its role during the pandemic to direct patients to the most clinically appropriate service, including Emergency Departments, an Urgent Treatment Centre, a GP or mental health professional.