The Prime Minister believes it would be “fitting” for Mr Zelensky to speak to the millions of people set to watch the final on Saturday, particularly as the UK is hosting it on behalf of war-torn Ukraine.
The European Broadcasting Union (EBU) barred the leader from making a video appearance over fears it would “politicise” the competition.
Mr Sunak’s spokesman said on Friday: “The Prime Minister believes it would be fitting for President Zelensky to address the event and was disappointed by the decision from the EBU.
“The values and freedoms that President Zelensky and the people of Ukraine are fighting for are not political, they are fundamental.
“Eurovision themselves recognised that last year when they rightly suspended Russians participation from the competition.”
Mr Zelensky was expected to implore the event’s audience of more than 160 million people to back his country in its fight against Vladimir Putin’s army.
But EBU, an alliance of 112 member organisations which organises the annual contest along with the host broadcaster the BBC, refused.
The EBU’s management team said Mr Zelensky had “laudable intentions” but that “regrettably” his request was against the rules.
A spokesman said: “The Eurovision Song Contest is an international entertainment show and governed by strict rules and principles which have been established since its creation.
“As part of these, one of the cornerstones of the contest is the non-political nature of the event.
“This principle prohibits the possibility of making political or similar statements as part of the contest.”
Ukraine’s Kalush Orchestra won last year’s contest but, because of Russia’s invasion, hosting duties were awarded to the runner-up, the UK, instead.
Ab EBU spokesman added: “No fewer than 11 Ukrainian artists, including last year’s winners Kalush Orchestra, will be performing.
“Additionally, 37 locations around Ukraine will feature in the short film postcards that introduce each of the participating artists before they take to the stage.
“We believe that this is the best way to reflect and celebrate Ukraine’s Eurovision Song Contest win and show we are united by music during these hard times.”
It comes as those hoping to attend the event in person faced travel misery as train drivers stage their latest strike in a long-running pay dispute.
Members of the drivers’ union Aslef walked out on Friday at more than a dozen train operators, crippling services on the day of the son content’s semi-final.
On Saturday Rail, Maritime and Transport union (RMT) members were due to stage their latest round of industrial action on the day of the Eurovision final.
Aslef General Secretary Mick Whelan hit out at claims that the strike was timed to clash with Eurovision.
“Strangely enough, I don’t really watch Eurovision, I didn’t know they had semi-finals,” he said, adding that “ if we were targeting Eurovision we would have done Friday, Saturday and Sunday”.