Wyle Cop (uphill) and High Street will be closed to all traffic between 11am and 4pm on weekends, and closed to all traffic other than buses, taxis and cyclists between 11am and 4pm, Monday to Friday.
Milk Street and the southeast side of The Square will also be closed to traffic from 11am to 4pm every day.
Changes to waiting and loading restrictions are also planned in a bid to free up space for pedestrians and cyclists during the main trading hours.
A public consultation is set to be carried out this autumn to ask residents, business and visitors if the measures should remain on a permanent basis.
High Street, Shoplatch and Wyle Cop (uphill) are currently closed to all traffic from 11am to 4pm each day to encourage social distancing.
During the closures, traffic will be encouraged to use the inner ring-road to travel around the town centre. Motorists will be advised to only use the historic Town Walls for access and not as a through route.
Concerns have previously been raised over the damage being caused to the historic walls by the added traffic while the town centre is closed, as well as the added danger to pedestrians near the Quarry.
Steve Charmley, Shropshire Council’s cabinet member with responsibility for highways, said: “As restrictions come to an end, we are taking a proactive approach and trialling measures to create the best possible environment for the town centre to thrive.
“The aim of the measures is to trial a potential reshaping of the physical public realm and traffic management arrangements within the town centre, allowing opening up of additional public space whilst promoting pedestrian safety, active travel alternatives and movement around the town.
“Over the past 12 months, the priority has been to enable social distancing in the town centre, but reducing through traffic and improving the pedestrian experience is also a long-term aspiration of the Shrewsbury Big Town Plan.
“We feel that continuing to restrict general vehicle access from 11am to 4pm will greatly benefit the town centre environment during the busiest part of the day, and by allowing buses to access the High Street during the week, we are prioritising public transport as part of the town’s recovery.
“At weekends between 11am and 4pm, buses will be directed either around the town centre or along Town Walls, which will allow the town centre to be a traffic-free zone and give hospitality businesses the opportunity to embrace the outdoor cafe culture which has been so successful in recent months.
“We will continue to monitor the situation and will ask for people’s opinions later in the year about longer-term arrangements – and we’ll continue to review and consider any further measures to reduce through-traffic on Town Walls.”
Shropshire Council’s cabinet will be asked to consider the measures, and approve the consultation, when it meets on July 21.
Seb Slater, executive director of Shrewsbury BID, said: “We welcome this approach, which aims to continue supporting the recovery by prioritising the pedestrian experience, as well as providing additional outdoor space for businesses.
“Full pedestrianisation of High Street on the weekends between 11am and 4pm will support an exciting programme of weekend activities and events which we have planned for locals and visitors to enjoy over the summer.
“All car parks will remain fully accessible for customers to use at all times with buses returning to the High Street on weekdays.”
He added: "We support proposals to restrict through traffic on the historic Town Walls route which has been discussed by range of local stakeholders within the Recovery Taskforce. Town Walls is a pedestrian route used by many residents, students and visitors each day and further protection from through traffic which does not stop in the town centre is needed.
“We will be encouraging all businesses to share their feedback as part of the public consultation scheduled for the autumn which will determine the long-term plan.”
A statutory consultation for the required experimental traffic regulation order is already underway and can be found on the Shropshire Council website.
Meanwhile, the suspension of the bus lane on Castle Street will remain until 30 September, and measures that have seen Victoria Quay pedestrianised at certain times will end this Sunday night. Measures in place on Town Walls will be retained.