“Their service and sacrifice will never be forgotten,” he said in a statement.
Defence Secretary John Healey said he was “devastated by the death of a UK service person in Ukraine”.
“My thoughts are with their family, friends and colleagues as they grieve for a loved one.”
It is not known which service the individual served in or what his role was.
The BBC understands the incident is not thought to have been caused by hostile fire.
The MoD said it would not comment further.
The UK government has never confirmed the number of service people in Ukraine, but has previously acknowledged a small number in the country to support Ukraine’s armed forces and provide security to diplomatic personnel.
It is the first time a UK military death has been publicly announced since February 2022.
The chairman of the Defence Committee, Tanmanjeet Singh Dhesi, said: “This tragic incident is a stark reminder of the risks faced by those who serve our country, even when operating away from the front lines. I pay tribute to their professionalism and commitment.”
Shadow defence secretary James Cartlidge said he was “deeply saddened to hear the tragic news that a member of the UK armed forces died this morning in Ukraine”.
“My sincere condolences to his family and friends at this difficult time.”
Fighting has raged in Ukraine since Russia launched a full-scale invasion more than three years ago in February 2022.
Efforts to negotiate an end to the war have intensified in recent weeks, including a visit by Ukraine’s President Volodymyr Zelensky to Downing Street on Monday where Sir Keir pledged the UK’s support for Kyiv in achieving “a just and lasting ceasefire”.
The meeting was part of a push by Zelensky to deter the US from backing a peace deal which includes major concessions from Kyiv, and which allies fear would leave it vulnerable to future invasion, with Ukraine set to present alternative proposals to the White House.
