Mr Sunak served Christmas dinner to servicemen and women at the Tapa military base.
He said he was sorry that they would be missing the festive period with their families at home and thanked them for their “sacrifice” and “extraordinary” service in a year in which the world has been rocked by Russia’s invasion of Ukraine.
Donning an apron, Mr Sunak ladled turkey and vegetables on to soldiers’ plates as his Estonian counterpart Kaja Kallas served pigs in blankets next to him.
In impromptu remarks to troops gathered in the canteen afterwards, he said: “What you do is extraordinary.
“I know you’re going to miss being with your family and friends over Christmas, and I’m sorry about that, but I appreciate your sacrifice, as does everyone else back home.
“The professionalism, the expertise, the intelligence that you bring to your job every single day and the enormous impact on the continent — it means that we can sleep safe at night, and the security and peace of mind is really something that we will never, ever take for granted.
“So, have a fantastic Christmas, thank you for everything.”
A look at the Nato military alliance — in pictures
Earlier, Mr Sunak spoke to military personnel including the King’s Royal Hussars, an armoured cavalry regiment.
The King’s Royal Hussars took over the rotating leading role in Nato’s enhanced forward presence multinational battlegroup in Estonia in the autumn.
Surrounded by an array of tanks in a vast hangar, the Prime Minister laughed and joked with the troops, commiserating with a French soldier over the World Cup final result.
More than 1,000 British armed forces personnel are deployed across Estonia and Poland as part of Operation Cabrit.
The UK doubled its presence in Estonia in response to the build-up of Russian forces near Ukraine earlier this year.
The footprint will be nearly halved next year as some forces are redeployed to other countries.
Challenged over the reduction by Estonian broadcasters, Mr Sunak stressed the UK’s continuing commitment to the nation’s security.
Putin 'planning for a long war' in Ukraine, says Nato chief — video
“What we are actually doing is increasing the capability of our presence here, increasing the lethality of it,” he said.
“We’re keeping other resources at readiness so they can be deployed here at a moment’s notice and we’re going to increase the amount of exercises that we do here in Estonia. You’ll see that next year when helicopters arrive.
“What I would say is we remain absolutely committed to Estonia, to the Nato forward presence we have here.”
Mr Sunak began his whistle-stop trip to the Baltic states in Riga, Latvia, earlier on Monday.
There, he called on fellow leaders of northern European nations to stand firm in their support for Ukraine at a summit of the Joint Expeditionary Force.