Work on gas pipes, which is expected to last up to eight weeks, will see High Street, and Shoplatch closed to traffic, and Wyle Cop closed to uphill traffic.
A diversion route for traffic heading from the Wyle Cop to Shoplatch direction, has been put in place taking vehicles around Town Walls.
Gas network Cadent is replacing iron mains pipes with plastic ones.
Shropshire Council has said that access will be maintained for businesses, residents and emergency vehicles, and that all car parks will be available.
The authority plans to use the closure to carry out its own work, removing the need for a second disruptive closure.
A spokesman for the council said: "While the road is closed for the work to take place contractors working for Shropshire Council will take advantage to carry out minor maintenance works.
"Once the pipes are in the ground, Shropshire Council will continue a major facelift of the street’s paving."
While the work is carried out Shrewsbury BID is to transform Shoplatch into a ‘pocket park’ to encourage people to spend more time in the town centre.
The park will feature artificial turf and flowers, with deck chairs, live music and activities replacing the vehicles which usually use the road.
As a result of the closure there will bechanges to the park & ride.
The Harlescott service will not serve stops at High Street, Shoplatch, Barker Street and Chester Street.
The Oxon service will not serve stops at High Street, Shoplatch, Barker Street and Frankwell (return), and the Meole Brace service will not serve stops at High Street and Shoplatch.
Craig Horrocks, who heads up Cadent’s gas mains replacement programme in the West Midlands region, said: “We are investing in new gas pipes so that local people can continue enjoy safe and reliable gas supplies until the end of the century.
“The pipes have been selected for replacement due to their age and in accordance with the prioritisation policy agreed with energy watchdog Ofgem and the Health and Safety Executive.
“This essential work has been carefully co-ordinated with Shropshire Council so that any newly resurfaced areas are not disturbed by planned gas work in the near future. We appreciate this work may be disruptive and will do everything we can to minimise the disruption.
“Access to businesses will be maintained. Our customer team will liaise with local residents and businesses to answer questions and respond to any concerns.”
Dan Green, assistant network management officer with Shropshire Council, said: “Cadent have a regulatory obligation to replace gas mains deemed ‘at risk’ within a set timescale.
"Work to replace the gas main on Shoplatch has become more urgent, meaning that the work is now required for completion this year.
"Given the planned resurfacing of Pride Hill and Mardol Head it seemed logical that the gas main replacement work was brought forward to pre-date this resurfacing work.
“Shropshire Council has contacted other utility companies to ask that any other planned maintenance works are undertaken while the road is closed, and will carry out its own minor maintenance works during this time. This will reduce longer-term disruption to what is a busy location and reduce the need for future closures.”