The camp has grown by 6,000 people since October, and doctors say a humanitarian crisis is imminent.
About 220,000 Rohingya live in Bangladesh.
Described by the UN as one of the most persecuted minorities on earth, thousands of Rohingyas from Myanmar's northern Rakhaine state stream across the border into Bangladesh every year.
Those living outside of an official Rohingya camp in Kutu-palong on the Myanmar border have been subjected to "unprecedented levels of violence", MSF said in the report.
Paul Critchley, the MSF head of mission in Bangladesh, told Al Jazeera: "We are seeing what appears to be a violent crackdown, which is driving the Rohingya out of the community.
"We are seeing what appears to be a violent crackdown, which is driving the Rohingya out of the community"
MSF head of mission in Bangladesh
"We have treated many patients who have been victims of violent attacks, who tell us they have been beaten by police ... arrested, handed over to the Bangladesh border security and forced to swim back to Myanmar."
Bangladesh recognises 28,000 Rohingya as official refugees, who live in official camps under the supervision of the UN.
This figure is a fraction of the estimated 220,000 unofficial refugees, MSF says.
There are an estimated 700,000 Rohingya in Myanmar, where they are not recognised as citizens and have no right to own land.
They are also forbidden from marrying or travelling without permission.
Police on the border with Myanmar told the AFP news agency on Thursday that although a crackdown on unregistered Rohingya was under way, there had been no police brutality against the refugees.
Asked about MSF's findings, Rafiqul Islam, chief of the local police in Kutu-palong on the Myanmar border, said: "Any refugees who go to seek medical treatment got hurt by each other - they are always fighting."
The crackdown was necessary to prevent further mass migration.
"If we don't stop them, the floodgates will open," he said.