The bistro at Onyx Business Park off Manvers Way was taken over last December by chef Rhys Blessed and business partner Chris Crane.
Previous landlord Mark Perry had left under a cloud after claiming bankruptcy and people booked on for Christmas Day lost their deposits.
A statement from Chris and Rhys confirmed the closure was a result of being unable to afford rent payments.
"In a nutshell the rent and rates charged on such a small unit are too high," they said.
"We applied for help with rates relief with us being a first time business but unfortunately nobody could help.
"We're still in touch with customers and are hopefully taking bookings forward.
"If that's not the case any deposits paid will be refunded as soon as possible."
They are offering to refund people but say they will accommodate bookings at new premises yet to be announced.
A post on the Bistro's Facebook site on Wednesday evening added: "We're sorry to say that Bistro 63 is no more.
"It all happened sooner than we thought so apologies for any bookings we'll miss but we have something in the pipeline for a bigger place, (an offer we couldn't refuse) so watch this space."
People with bookings should email firstname.lastname@example.org
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