Following a meeting with Argentine president Cristina Kirchner, the Oscar-winning actor urged Britain to join UN-sponsored talks over what he called "the Malvinas Islands of Argentina".
The 51-year-old said: "I hope that diplomats can establish true dialogue in order to solve the conflict.
"The world today cannot tolerate ridiculous demonstrations of colonialism. The way of dialogue is the only way to achieve a better solution for both nations."
Penn, who was made an official ambassador to Haiti last month, is well-known for his political and social activism.
Last October, he joined Egyptian protestors in a demonstration at Cairo's Tahrir Square and also blasted the 'racist' Tea Party in America, claiming that the right wing political party wanted to "lynch" US president Barack Obama.
Britain has rejected Argentina's claims that it was increasing military power on the South Atlantic island as the 30th anniversary of the Falklands War nears.
Tensions between the two nations have simmered over recent months, with UK Prime Minister David Cameron and Kirchner trading tough statements.
Penn told reporters: "I think that the world today is not going to tolerate any kind of ludicrous and archaic commitment to colonialist ideology."
But The Tree of Life star's intervention in the dispute has been met with bemusement among inhabitants of the Falkland Islands.
Lisa Watson, the editor of Falklands newspaper the Penguin News, wrote on Twitter: "Ha Ha if Penn supported UK Brits would probably ask what gives an actor the right to have an opinion on the Falklands?"