The criticism comes as the country falls back into international pariah status due to its treatment of the ethnic Rohingya minority in the country's western Rakhine state.
More than 670,000 Rohingya Muslim refugees have fled Buddhist-majority Myanmar into neighboring Bangladesh since August 2017, bringing with them stories of murder, rape and the destruction of villages at the hands of the Myanmar military.
The Yorkshire team announced the promotional tour on its website earlier in the week.
The team is scheduled to compete against the Myanmar national side and a select league club in two fixtures in May, following the conclusion of the English domestic season.
UK Shadow Sports Minister Rosena Allin-Khan condemned the tour in a letter to the club's chairman, Andrea Radrizzani.
In the letter the Labour politician said that the "morally corrupt" action would legitimize the Myanmar government's refusal to engage diplomatically on what the UN has called the ethnic cleansing of the Rohingya.
The Leeds United tour is being planned in partnership with AYA Bank, a Myanmar financial institution.
In a statement released by the club, Radrizzani said: "It has never been my intention, nor that of the club, to get involved in a political debate in Myanmar.
"However, if because of the tour we further highlight the ongoing serious issues in certain areas of the country, then maybe that is a positive thing.
"I have spent over 10 years living in Asia and Myanmar is a country I have visited on many occasions. I am aware of the serious issues within the country, but I also know that it is a beautiful place filled with incredibly warm and welcoming people. It is somewhere very close to my heart.
'Heartbreaking' details of massacre recounted
Allin-Khan, who represents the London borough of Tooting, says she recently visited Rohingya refugee camps in Bangladesh and heard eyewitness accounts of massacres of the Muslim minority by Myanmar government troops.
"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."
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. They must rethink it, history will judge them to be on the wrong side of this."
Some fans of the club have also taken to social media to agree with her stance.
"Last week we supported (rights group Amnesty International) over refugee contribution to football. Now a proposed tour to a country involved in ethnic cleansing and mass refugees. My club LUFC needs to get a grip!"
Another simply tweeted, "This tour is not in my name."
Call for club to use tour as 'leverage'
Amnesty International issued a statement calling it an "odd choice of country to choose to tour."
In the statement, Kate Allen, Director of Amnesty International UK is quoted as saying that "far too often sporting events have been used as a cheap PR tool to 'sportswash' the stain of a country's human rights record.
"We're not going to tell Leeds United where they should and shouldn't visit, but if the tour does go ahead, the club should use its leverage to call for an end to the crackdown and raise with the Burmese authorities the plight of the hundreds of thousands of families who have been brutalized and forced to flee their homes."
A statement from the club's supporters trust took issue with the tour, but from the perspective of safety. The British Foreign and Commonwealth Office (FCO), which advises on travel safety for British nationals, has warned would-be visitors to "check travel advice" before embarking on a trip.
The FCO advises against all but essential travel to some areas of the country, including Rakhine state.
The Leeds United Supporters Trust says it recognizes the "discontent" amongst fans but insists that the tour is non-political in nature.
The group says it views the tour as "an opportunity for Leeds United to be pioneers and break down barriers and build relationships with the people and business community within a country trying to emerge from a difficult past."
Leeds United, once one of the biggest, most successful teams in England, made it to the final of the European Cup in 1975 but since the early 2000s has fallen on hard times and has found promotion to the top-tier Premier League beyond its grasp.
The club currently sits in 12th place in the Championship, England's second-tier league.