The shop, in High Street, is among 95 branches of the chain which are ceasing trading.
The closures came after the appointment of joint administrators from BDO Stoy Hayward.
One of the administrators, Dermot Power, a business restructuring partner at the firm, said: "Despite a strong trading name and presence on the high street, Motor World has been a direct casualty of the current retail difficulties and the continuing squeeze on available credit."
Motor World was one of the UK's largest independent car care retailers and had 237 shops across the country.
The closure of the 95 branches has resulted in the loss of 300 jobs, but the administrators have sold the remaining 142 branches, saving 500 jobs.
Martin Waite of Bailey Capital which bought the shops said: "We remain acutely aware that difficult trading conditions will undoubtedly continue, but remain hopeful that we can move the business forward following the restructuring that has taken place and strengthening of the management team."
Motor World is the latest in a series of casualties in High Street, Stamford, which include the Get Boosted juice bar which closed in July and the Bargain Book Store and Pendulum Records which are due to close when their leases run out. Louisa's clothes shop and the Sugar Bowl restaurant closed earlier this year.
The vice-president of the town's chamber of trade Andrew Leech said the strength of Stamford's retail base was affected more by the general economic situation than the closure of individual shops. He said independent retailers - an area where Stamford was strong - tended to be more entrepreneurial than national chains. But they too were affected by challenges like rising energy costs and interest rates which undoubtedly resulted in less money in people's pockets.
But new retailers have opened in the town, including Orvis in St Mary's Street and Fat Face in High Street.
Mr Leech said: "Shops that fall vacant don't seem to stay empty for very long."