The incident happened near the southern Bangladesh border town of Naikhongchari on Saturday when Badiur Rahman crossed into the zone.
"His cow strayed inside the Myanmar border in no-man's land. He accidently stepped on a mine when he went there to fetch the cow," said Sarwar Kamal, a local government administrator.
The 45-year-old was rushed to a local clinic and later moved to hospital in the southern port city of Chittagong.
"His condition is very critical," said Marjia Khatun, a nurse.
Bangladesh border officials accuse Myanmar security forces of planting mines along border areas.
Border Guard Bangladesh commander Anwarul Azim said the area where Saturday's incident happened was unfenced and grazing cows very often strayed across.
"The Myanmar army planted those mines a while ago. Rahman accidentally stepped on one of those and lost both his legs," he told AFP.
Myanmar troops have been accused of waging an ethnic cleansing campaign against the country's Rohingya Muslim minority, nearly 700,000 of whom have fled to Bangladesh since last August.
Rights activists say the mines are aimed at preventing the refugees from returning to their villages.
"By planting these mines, the Myanmar army is trying to ensure that the Rohingya refugees would never try to return home," said Bangladeshi rights activist Nur Khan Liton.
"They don't care whether they are breaching international law," Liton said, adding that such acts were "crimes against humanity".
Since the violence erupted on August 25, several Rohingya have been killed in landmine explosions in no man's land.
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