The news has been greeted with dismay by the local community with residents seeing the venue as an important community hub.
A petition to save the café had been signed by more than 1,400 people on Wednesday morning.
The campaign has the backing of actor Antony Cotton MBE, who plays Sean Tully in Coronation Street.
The star, who is an ambassador and patron of several military charities, as well as president of the St James Royal British Legion, described the café as “a vital hub for so many in the Garrison”.
The not-for-profit NAAFI, an arm’s length body of the Ministry of Defence, said the café, which opened in March 2023, had been losing money and was not viable.
The company said in a statement: “Despite our best efforts, and although it has become a popular place to meet for many people (and paws!), it is no longer economically possible for us to continue operating in Catterick.
“The many financial factors, including rent, business rates, operational costs, and rising product costs, mean that the money lost is too vast to continue, however much we would love to keep the facility open.”
The statement added: “NAAFI’s main focus is serving our Armed Forces, and we operate as a business, not a charity, with all our surpluses going back in various ways to support UK Armed Forces.
“To continue operating Catterick cafe would mean losing money at an unsustainable rate, money that could be used elsewhere serving Defence communities in our locations around the world.”
NAAFI bosses say they will help find a new tenant for the unit, which has previously been a branch of Prezzo and an independent Italian restaurant.
North Yorkshire councillor, Kevin Foster, who represents the Hipswell and Colburn division, has held talks with NAAFI officials and is hopeful a new tenant can be found.
He said: “NAAFI have assured me that they want to do all they can to help someone else take it over, possibly as a community charity venture, but they are open to all ideas.
“By doing a charity or community thing, it would bring the outgoings right down to a minimum.
“The opportunity is there and they have promised that they will help someone with that transition if the right people can be found.
“There is a solution out there, but we just need to find it, and harness the potential.”
Cllr Foster said he had been assured that the café was not closing imminently.
He added: “Consultation has begun, but there is still a bit of time left to work out the best plan.
“If the community want it open, then NAAFI will help as much as they can.”
Anyone interested in potentially taking on the cafe can contact NAAFI at catterickenquiries@naafi.co.uk