The company told The Scotsman 12 staff had contracted the virus - 20 per cent of its staff in the capital.
It said most of the cases were confirmed after the operation was closed, when staff were told to get tested and self isloate.
The Rail, Maritime and Transport union claimed there had been no control measures in place such as distancing, and there had been a lack of personal protective equipment.
However, a spokesperson for Rail Gourmet said, “The health and safety of our colleagues and customers is paramount to us, and we follow strict safety measures, particularly with regards to Covid-19.
“Despite these measures, regrettably, a number of colleagues from our Edinburgh service centre tested positive for Covid-19.
"At least two people infected are colleagues who live together, so it was anticipated that the numbers would increase after closure, as is sadly unavoidable in a family environment.
"In response, we swiftly contacted our local health authority, took action to temporarily close the unit, and all colleagues who had been working the same shift were advised to self-isolate and arrange to be tested.
"We remain in dialogue with the health authority and are currently conducting an internal investigation into the cause of the infections.
“We have put alternative plans in place to ensure we can continue to service our clients and customers, and as soon as it is safe to re-open the service centre, we will do so.”
A spokesperson for LNER, which currently operates trains between Edinburgh, Glasgow, Inverness and London via the east coast main line, said: “The safety of our staff and customers is our top priority.
"We work closely with our suppliers across our route to ensure appropriate safety measures are in place.
"The impact on our services is minimal and we continue to work hard to provide the experience all our customers expect from us.”
Rail Gourmet, which took over British Rail’s train catering when it was privatised in 1995, also supplies operators such as TransPennine Express, Great Western Railway and Grand Central.