The company said it had not been able to make the Little Waitrose shop at the top of Pride Hill "profitable in the long term". Thirty-four workers are affected.
The closure is one of four announced by the company today, and will be a blow to Shrewsbury having taken up a prominent space on the town's main street.
The shop will close on December 6 according to the company, along with stores in Caldicot and Ipswich Corn Exchange, while its Wolverhampton store is being sold to Tesco.
Bérangère Michel, partner & executive director, customer service for the John Lewis Partnership, said: “Closing any of our shops is always a last resort and is not a reflection on the dedication of our partners in Caldicot, Ipswich Corn Exchange, Shrewsbury and Wolverhampton. Sadly, we have not been able to find a way to make these shops profitable in the long-term, despite the hard work of everyone involved.
“Our priority now is the wellbeing and future of our partners in these shops. We will do everything we can to support them and explore opportunities wherever possible for those who may wish to remain with the partnership.”
A statement from the company added: "The announcements form part of an ongoing review of the Waitrose store estate, which began in 2017. We have found trading challenging in these four shops and, despite the best efforts of partners, we have not been able to find a way to make them profitable in the long-term.
"It is expected that Caldicot, Ipswich Corn Exchange and Shrewsbury will all close at the end of trade on 6th December and Wolverhampton will close at the end of trade on 31st December."
In its statement the John Lewis Partnership said it would support those at risk of redundancy with up to £3,000 for retraining – provided they had two or more years of service.
It said: "The John Lewis Partnership has also made a commitment to provide support to those partners at Caldicot, Ipswich Corn Exchange and Shrewsbury who are at risk of redundancy through a unique retraining fund. This will contribute up to £3,000 towards a recognised qualification or course for up to two years for any of the 124 partners with two years’ service or more. They will also be given access to a three month support programme with an outplacement specialist to help with CV writing and interview skills.
"In addition to statutory redundancy payments, partners who have worked with the business for more than a year will be entitled to partnership redundancy pay, which equates to two weeks’ pay for every year of service, regardless of age. Those with less than one year’s service who leave on grounds of redundancy will receive an ex-gratia tax-free payment equivalent to one week’s contractual pay."
The company said it would also be providing an investment fund for three of the communities affected – including Shrewsbury.
The statement said: "The John Lewis Partnership has committed more than £200k from its Partnership Community Investment Fund to help support those communities affected by the closures. The fund is designed to help projects that support re-training and further education of local people and local projects that drive economic growth and support young people through training and helping to find employment. Further details on how to apply will be provided in the coming weeks."