In an Instagram post, the brothers said they had been left with no choice but to walk away from the site after being unable to negotiate suitable terms with their landlord when renewing their lease.
Juke & Loe's final service will be on 28 May.
"It is with a heavy heart that we make this announcement," the brothers wrote.
"Juke and Loe will close its doors on the 28 of May this year. Our five-year lease is up and despite negotiations with our landlord we are unable to come to a new agreement that benefits and protects the business and staff, this leaves us with no choice but to walk away."
The pair added that they on the lookout for other premises in and around Sheffield.
Juke & Loe has been recommended in the Michelin Guide Great Britain and Ireland for the last two years, although it doesn't hold either a Michelin star of Bib Gourmand.
The restaurant, which bills itself as offering 'relaxed, eclectic, seasonal and contemporary dishes', has also been a critical sucess, with The Observer's Jay Rayner recently praising its 'delightful and impressive cooking'.
"It’s been a tremendous five years with highs and lows, we have enjoyed great success with recognition from guides, the national press and food critics alike," continued Joseph and Luke.
"Of course, none of this would be possible without the support we have received from you, the customer. It’s been a fantastic journey and we hope to welcome you all along to our next venture as soon as possible.
"Above all, our thanks and appreciation go out to the staff, past and present. We couldn’t have asked or wished for better people to share this journey with. Your hard work and dedication have reminded me why we fell in love with this industry in the first place."