The company has confirmed its Pride Hill restaurant will shut its doors for the final time in February when the lease expires.
The restaurant has been a feature of Pride Hill for more than 30 years and part of the building which is currently home to the fast-food chain dates back to the 13th century – making it one of the oldest buildings in the world to house a McDonald's restaurant.
The company says it remains committed to the county and will retain its two other drive-thru restaurants at Meole Brace Retail Park and on Battlefield Road.
The company said all members of staff will be offered jobs in other restaurants.
A spokesman for the company said: "We are sad to confirm that our Shrewsbury restaurant will close on the February 25 after 34 years of trading when the lease expires. This decision has not been taken lightly but unfortunately the building is not suitable to meet our future plans.
"All employees will be offered roles in neighbouring restaurants.
"We will continue to have a strong offering in the town, with two other drive-thru restaurants in Shrewsbury, and remain committed to the Shropshire area."
The restaurant has been popular with students from the town's colleges and people enjoying the night-time economy.
Local councillor Andrew Bannerman said: "In one sense nobody likes to see a business closing.
"This has been one that has been popular with many people. In another sense the fact it was open 24 hours on Fridays and Saturdays has been difficult in certain respects."
Councillor Bannerman said he was confident a new tenant would be found and praised Shrewsbury's resilience when it comes to retail.
He said: "At the moment Shrewsbury seems to have survived the trouble in the retail economy remarkably well.
"It is a place people still like to come into whereas many high streets are suffering all over the country.
"I am particularly proud of the independent shops which I think are a distinctive feature of our town centre."