A boy of 15 being treated in Bangladesh lost both legs while a woman at the same hospital said she had trodden on a landmine after being fired on.
The area was mined in the 1990s but Bangladeshi sources say Myanmar's army recently planted new mines - an allegation denied by Myanmar officials.
More than 300,000 Rohingya have fled a brutal security crackdown in Myanmar.
On Monday UN human rights chief Zeid Raad al-Hussein said that a "cruel military operation" was taking place, calling it "a textbook example of ethnic cleansing".
The Rohingya, a stateless mostly Muslim minority in Buddhist-majority Rakhine, have long experienced persecution in Myanmar, which says they are illegal immigrants.
Bangladesh's Prime Minister, Sheikh Hasina, is due to visit one of her country's main refugee camps for Rohingya. She said earlier that Myanmar had to solve a problem of its own making.
The White House has called on Myanmar to respect the rule of law and end the displacement of civilians.
Aung San Suu Kyi, Myanmar's de facto leader, is facing mounting criticism for failing to protect the Rohingya.
'Suffering so much'
On Sunday the human rights group Amnesty International accused the authorities of laying landmines at border crossings used by fleeing Rohingya.
Bangladeshi government sources made the same allegation speaking to Reuters news agency last week.
The hospital visited by the BBC has seen an influx of people with landmine injuries, doctors say.
The 15-year-old boy, Azizu Haque, arrived with his legs destroyed. His brother, in another hospital, suffered the same fate, his mother says.
"Their injuries are so bad it's as if they are dead," she told the BBC. "It's better that Allah [God] takes them, they are suffering so much."
The injured woman, Sabequr Nahar, says she fled Myanmar because the military had been targeting her community, and she was crossing the border with her three sons when she stepped on a landmine.
"We'd been fired on, shot at, and they planted mines," the 50-year-old said.
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