The Commander Medical, British Forces Cyprus has told Forces News there is a "robust plan" in place to deal with coronavirus.
Cyprus has already announced its first two confirmed cases of COVID-19.
Nearly 6,000 British military personnel and their dependents are based on the island.
Cyprus' health ministry briefly advised all British visitors to self-isolate upon arrival in the eastern Mediterranean country for a two-week period, whether or not they had any coronavirus symptoms.
The UK had for a short time been upgraded to a 'category two' nation, meaning travellers would have to self-isolate, regardless of whether they had symptoms or not.
Britain instead remains a 'category three' country, meaning only those with COVID-19 symptoms need to self-isolate and seek medical advice - the same as in the UK.
It is home to two British Sovereign Base Areas which in total cover 98 square miles.
British troops are also part of the United Nations peacekeeping mission along the buffer zone between the Greek and Turkish sides of the island.
"The UK remains classified as a 'category three' country and this means that anybody planning to travel to Cyprus from the UK can carry on," said Group Captain Sonia Phythian, Commander Medical, British Forces Cyprus.
"Our aim is to absolutely look after our people, whether you are in uniform or not.
"We are aware that there have been some confirmed cases of coronavirus on the island of Cyprus but we want to reassure everybody that the risk remains low and we have a robust plan to protect you."
Countries currently named in category two by the Cypriot government include Germany, France and China - excluding Hubei province where the coronavirus outbreak began.
Italy, Iran, South Korea and Hubei province are all named in category one.
Italy, which has more than 9,100 cases of coronavirus, has extended travel restrictions to the whole country, with soldiers and police enforcing the bans.
Last week, the UK Minister for the Armed Forces James Heappey visited RAF Akrotiri and told Forces News the military is "ready" to deal with COVID-19.
In the UK, the Government has said the British Army is "ready to backfill" for the police if required in a worst-case scenario.
So far, six people have died from coronavirus in Britain.