The band says seeing atrocities against Rohingya people on the Burmese leader's watch "breaks our hearts"
U2 have called on Myanmar's de-facto leader Aung San Suu Kyi to fight harder against violence inflicted by the nation's own security forces.
Burmese police and army launched a violent crackdown in the northern Rakhine state following attacks by Rohingya insurgents on police posts in August.
It is believed that thousands of people in the state have been killed or tortured by security forces.
According to the UN, more than 600,000 Rohingya Muslims have fled to Bangladesh since late August to escape the violence.
Aung San Suu Kyi - Myanmar's State Counsellor, a role that effectively positions her as head of government - has faced widespread international criticism for her response to the situation in her country.
Members of U2 are well known as high-profile supporters of the Nobel Peace Prize winner, with the band having repeatedly called for her release during her time as a political prisoner.
However, the musicians have now posted a lengthy plea aimed at the Burmese leader - saying they had tried several times to reach out to her directly.
They say they 'punched the air' when she was released, and suggest 'we Irish could not have been more proud' when she visited Dublin in 2012.
They had been expecting to speak to her this week, but the call is now not expected to happen.
In a statement jointly signed by Bono, The Edge, Adam Clayton and Larry Mullen Jr, the band members write: "What has happened this year, and in particular these past months – this, we never imagined.
"Who could have predicted that if more than 600,000 people were fleeing from a brutal army for fear of their lives, the woman who many of us believed would have the clearest and loudest voice on the crisis would go quiet.
"For these atrocities against the Rohingya people to be happening on her watch blows our minds and breaks our hearts."
The musicians acknowledge that Mrs Suu Kyi faces complexities that "the outside world cannot understand" - but also say the complex situation in Myanmar should not require her to compromise her ideals.
However, they also argue that anger cannot solely be directed in the Nobel laureate's direction, suggesting that plays into the hands "of those who are carrying out the violence".
The band explains: "Min Aung Hlaing is not a widely recognised name outside Myanmar - it should be. This man is the Commander General in Chief of the Defence Services who answers to no-one when a security threat is declared.
"While this in no way excuses her silence, Aung San Suu Kyi has no control, constitutional or otherwise, over his actions, and it is he who has authorised and overseen the terrorization of the Rohingya people under the guise of protecting Myanmar from terrorism. Condemning her and ignoring him is a mistake."
Last week it was reported that Mrs Suu Kyi made her first visit to Rakhine state since the violence broke out, meeting with some of the remaining Rohingya villagers.