The 15-year-old lost both his legs in the blast near the border. Myanmar is one of the last countries in the world to actively use landmines.
The explosion and cuts and shrapnel wounds across most of his body had left Haque in agony.
The youth remained in a desperate state despite several operations and an administrator at a charity hospital in Cox's Bazar, focus of the mounting Rohingya refugee crisis, confirmed Haque passed away there early today.
Haque's mother, Rashida Begum, spent days at the bedside of her son. He could barely muster enough energy to ask for a fruit juice. She did not have enough to pay for it anyway.
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In the hours before his death, she tearfully recounted to AFP how the family had escaped their home village only to face devastation at the frontier.
The family are among almost 400,000 Rohingya Muslims who have sought refuge in Bangladesh from violence in Buddhist- dominated Myanmar's Rakhine state that started August 25.
"Everyone was in a rush. Nobody could look out for others as the Burmese were chasing us from behind and burning the village," the mother of four said.
They were in sight of the Bangladesh frontier when Azizul Haque set off the landmine.
"We heard a huge explosion as Azizul stepped on the mine," said the mother. "I saw his two legs blown away."
While many Rohingya refugees have recounted tales of torture and rape by Myanmar troops and Buddhist militias as they escaped, landmines are the latest deadly threat to come to light.
"Since September 3, we have heard at least 12 landmine explosions. At least three people were killed and seven were injured in the blasts," Border Guard Bangladesh Commander Manzurul Hasan Khan told AFP.
Haque is the fourth known death.
"All indications point to the Myanmar security forces deliberately targeting locations that Rohingya refugees use as crossing points," said Tirana Hassan of Amnesty international.
"This a cruel and callous way of adding to the misery of people fleeing a systematic campaign of persecution," she said.
The 1.1-million strong Rohingya have suffered years of discrimination in Myanmar, where they are denied citizenship even though many have long roots in the country.
Border guards let Haque's family enter when they carried the stricken boy to the fence.
"We rushed him to a nearby Doctors Without Borders clinic and they referred us to this hospital," said his mother Rashida.
Surgeons conducted multiple operations on Haque, but said his chances were never good.
Several others, including Haque's brother were injured in the same mine incident.
Sabekun Nahar, 50, suffered leg injuries after she stepped on a suspected landmine near where Haque was blown up.
"I wonder how I will ever walk again," she said, tears welling in her eyes.