Dr Allin-Khan reacted with "anger and dismay" after Leeds announced plans to play an All-Star XI in Yangon on May 9 and Myanmar's national team in Mandalay on May 11.
Myanmar's governing regime has been accused of ethnic cleansing of Rohingya Muslims, including rape and slaughter, said Dr Allin-Khan, who posted her letter to Leeds owner Andrea Radrizzani on Twitter.
"It is morally corrupt for a football team to partake in a post-season tour to promote a country which carries out state-sponsored mass murder," Dr Allin-Khan said.
"Do you honestly believe your fans want the club they have supported all their lives to start endorsing a state carrying out such awful atrocities on innocent people?
"It is imperative that Leeds United is on the right side of history. I sincerely hope you will reconsider your post-season tour."
Amnesty International has also criticised the Sky Bet Championship club's decision to tour the south-east Asian country.
"It certainly seems like an odd choice of country to choose to tour," said Amnesty International UK director Kate Allen.
"The last year has seen the human-rights situation in Myanmar deteriorate dramatically.
"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 Myanmar authorities have continued the brutal crackdown despite a global outcry.
"Far too often sporting events have been used as a cheap PR tool to 'sportswash' the stain of a country's human rights record."
Violent clashes between Myanmar's government troops and militants are on-going in several areas of the country.
Some Leeds fans have voiced their anger on social media, while the Leeds United Supporters Trust said it was "a strange and controversial choice, given the dangerous political climate Myanmar currently finds itself in".
LUST chairman Steve White told Press Association Sport: "We're mainly concerned with the welfare of fans because no matter where Leeds United play, whether on a post-season tour or a pre-season tour, there will be fans going, simple as that.
"Our message to fans would be 'don't go without making an informed decision'. Get every bit of information about the situation that you can and take advice from the appropriate people and then make your decision.
"It's not a tour that I would have chosen personally."
Leeds United Supporters Club secretary Chris Hall added: "It seems a strange decision for Leeds to be playing two friendly games there."
The Leeds United Supporters Club of Scandinavia, which claims to represent 5000 fans, has called for the tour to be cancelled.
"Scandinavian Leeds United fans ask the club rethink the plan to travel to Myanmar to play two games there in May," LUSCOS said on Facebook.
"This trip will hurt Leeds United's reputation. We fear that the club, players and fans (will appear to) support to the powers in Rangoon, which have a lot to answer for on human rights in general or abuse against civilians.
"We'd like the club to stay away. We don't see any sporting reasons for the trip.
"This Myanmar trip puts the club and its rich traditions in a bad light. The club should turn."
Regional MEP Amjad Bashir also spoke out against the planned trip, labelling it "misguided".
Bashir, who has campaigned for the protection of Myanmar's Rohingya minority, said: "By playing football there, they would be giving succour to a brutal regime and aligning themselves with the perpetrators of ethic cleansing and genocide."
Leeds managing director Angus Kinnear said the club was "delighted" to support Myanmar's ambitions for grassroots and elite football development.
"Myanmar is one of the fastest growing nations in south-east Asia and is passionate about English football," Kinnear said.
"This tour gives us an opportunity to meet new fans of football who will hopefully support our journey back to the Premier League in the coming years."
Two companies owned by Leeds chief Radrizzani, Aser and Eleven Sports, have business partnerships in the region and there are expected to be commercial benefits from the tour.
Leeds will be holding football clinics with the Myanmar Football Federation Academies in Yangon and Mandalay.
A Leeds spokesman told Press Association Sport that the club is liaising with the Foreign Office and will avoid any areas of conflict. Further advice and travel details will be released for Leeds supporters, the club said.