The Elland Road side announced on Tuesday morning that they would be visiting the Southeast Asian country for two friendly matches, including a game against the national side.
The United Nations and rights groups say almost 700,000 Rohingya Muslims have fled to Bangladesh since a military operation in Rakhine state began in August.
The backlash was nearly immediate with the United Kingdom's Rohingya community damning the statement as "disgraceful".
"On my visits to the camps in November, I spoke to a village Imam who described, in heartbreaking detail, how he witnessed all the men from his village of 3,000 people in Myanmar being slaughtered and dismembered, the women being raped, and babies and young children being thrown, alive, onto burning fires".
'I am aware of the serious issues within the country, but I also know that it is a lovely place filled with incredibly warm and welcoming people. "It is somewhere very close to my heart", he added.
In a tweet highlighting her letter to Radrizzani, she wrote: "No UK club or organization should promote a country which carries out state sponsored mass murder".
"We simply want to use sport to do some good".
"We can't spread our values by turning our backs, we can only do this by engaging".
Allen continued, "We're not going to tell Leeds United where they should and shouldn't visit".
Shadow sports minister Dr Rosena Allin-Khan called the trip "morally corrupt".
Leeds United's Angus Kinnear: Has been out to Burma. Do you honestly believe your fans want the club they've supported all their lives to start endorsing a state carrying out such bad atrocities on innocent people?
Some Leeds fans have voiced their anger on social media, while the Leeds United Supporters Trust said it was "a unusual and controversial choice, given the risky political climate Myanmar now finds itself in". Leeds will not play in those areas.
More than 70 people were killed in Burma in August previous year after attacks on the police and military bases.
Amnesty International was quick to criticise the move.
The Myanmar military and government, including de facto leader, the Nobel prize victor Aung San Suu Kyi, have denied responsibility for the violence but recently the top United Nations human rights official called for Myanmar to be referred to the.
The decision to tour Myanmar has sparked security and health fears and raised ethical questions.
A statement from Amnesty International UK director Kate Allen said: "Far too often sporting events have been used as a cheap PR tool to "sportswash" the stain of a country's human rights record".
Political unrest has been a feature of life in Myanmar for several years.
'Hundreds of thousands of Rohingya have fled crimes against humanity in Rakhine State to neighbouring Bangladesh; those who remain continue to live under a system amounting to apartheid.
The club will play the matches on the May 9 and 11 against a Myanmar National League All-Star team in Yangon, and then against the country's national team in Mandalay.
AYA bank is owned by the Myanmar tycoon Zaw Zaw, who was blacklisted by the United States for being a crony of the former military regime.