Amnesty International have described the actions against the Rohingya Muslims in the northern state of Rahkine as genocide.
However Kyi has since drawn widespread criticism from around the world for her persecution or as United Nations assistant secretary-general for human rights, Andrew Gilmour calls it, "ethnic cleansing", of Rohingya people.
The Yorkshire team announced the promotional tour on its website earlier in the week.
The club will play two friendly matches against an MNL All Star Team and the Myanmar national team next month in Yangon and Mandalay, in a tour sponsored by AYA Bank.
Labour MP and shadow sports minister Dr Rosena Allin-Khan, who has been a prominent figure in the highlighting human rights abuses in Burma, wrote to Radrizzani on Tuesday.
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.
It all comes across as overly altruistic from Radrizzani, but surely simply by co-operating with the Myanmar authorities the club is turning a blind eye to the atrocities that are taking place on the government's watch.
Some Leeds fans have voiced their anger on social media, while the Leeds United Supporters Trust said it was "a odd and controversial choice, given the unsafe political climate Myanmar now finds itself in".
Some fans of the club have also taken to social media to agree with her stance.
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"Football is extremely popular in Myanmar and I believe the game we all love has the power to help developing nations by bringing people together, especially young people. 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".
A statement from the club's supporters trust took issue with the tour, but from the perspective of safety.
In those areas, the Foreign and Commonwealth Office (FCO) guidance is to "check travel advice before travelling".
The FCO advises against "all but essential travel" in some other areas of Myanmar, also known as Burma.
Leeds United's Angus Kinnear: Has been out to Burma.
Leeds were relegated from the English Premier League in 2004 and suffered years of financial woes.
But that has not deterred the end-of-season tour by the storied Yorkshire club, who are now mid-table in English football's second tier.