One of the closures will be in a concession Tesco store in Highbury, London.
Philip Clarke, chief executive of Tesco, bought a minority stake in the Harris + Hoole business last year, in a bid to attract shoppers to the supermarket.
The coffee company claims it still has the support of Tesco, and told The Telegraph that the closures did not indicate a weakness in performance.
Nick Tolley, co-founder of Harris + Hoole, told the paper: “Harris + Hoole is a fast-growing business. We have six more stores scheduled to open this year and the vast majority of our stores continue to perform strongly.
“However, like any business which has grown rapidly, some locations have performed better than others, so it makes sense for us to review those locations which have done less well, or where the lease is coming to an end.”
Harris + Hoole has over 40 locations in the UK, with a mix of high street stores and Tesco concessions.
Despite the closures, Tolley also outlined plans to expand by opening more stores on the high street and in the supermarket giant.
He said: “This review of our business was led by Harris + Hoole and we continue to have the full support of Tesco. Harris + Hoole is a start-up business still in its infancy - it was never our expectation to deliver a return from day one and many of our shops are still very new.
“It’s clear that our customers love the coffee, service and experience we offer, and this will be the bedrock of our future performance. Our working relationship with Tesco remains as strong as ever and we are looking forward to upcoming openings within Tesco stores later this year, as well as our planned standalone openings.”
A Tesco spokesperson said: “We continue to work successfully with Harris+Hoole. Feedback from customers in stores with Harris+Hoole coffee shops has been really positive and we look forward to more shops opening in the future.”
Clarke’s attempt to turn Tesco around has had a varied effect, and Dave Lewis is to replace him in the role of chief executive in October this year.