But the charges were swiftly denied by a government spokesman, who said Budapest "utterly rejects" the allegations.
In an interview with AFP, Christopher Stokes, one of MSF's directors, said the abuse appeared to be a way of deterring people from entering the country.
"This doesn't seem to be the behaviour of one or two policemen that fly off the handle," he said.
"It seems to be much more systematic and routine and organised."
Last week, Stokes visited locations near Subotica, a town in northern Serbia close to the Hungarian border, as well as MSF's facilities in Belgrade.
Although he said he had not himself witnessed any abuse, he interviewed "dozens" of migrants who had tried to enter Hungary in recent weeks and months and who were examined by MSF.
Migrants "get a kind of welcome package, if I could say cynically, from the border police that seems to consist of beatings and tear gas," Stokes said.
Police also "have people lie on the floor and walk on them and run on them with their boots," he said, with injuries such as bruising and cuts that were "pretty consistent" with such claims.
'Don't come to Hungary'
Last year, injuries treated by MSF tended to be "more open wounds and broken bones," Stokes said.
Now "there seems to be a tendency to hit them on the muscles, on other parts of the body, to create less obvious or visible marks but they are still detectable," he said.
Since the start of the year, MSF has also noticed police using the cold weather "as an element of extra punishment" -- confiscating shoes and other items of clothing and making people stand and walk in the snow.
They have also treated people with marks apparently caused by muzzled dogs pressing against necks.
"We are used to treating people who have suffered violence, and the stories we are hearing match with what we are seeing in our clinics," Stokes said.
"It seems to be to deter them from coming again so that people will pass on the message: don't come into Hungary."
'Trojan horse of terrorism'
But a spokesman for the government of hardline Prime Minister Viktor Orban rejected the allegations, insisting that migrants "are not being harassed".
"Hungarian police officers and soldiers are protecting the EU's Schengen borders lawfully and in compliance with EU and Hungarian regulations," Zoltan Kovacs told AFP by email, referring to Europe's passport-free zone.
"The police are performing their duties lawfully, professionally and proportionately, and they place special emphasis on treating migrants humanely and with respect for their human dignity," he said.
"Hungary treats those in genuine need humanely, and those waiting on its borders or on its territory receive fair treatment."
Hungary, which in 2015 erected a razor-wire fence on its southern border with Serbia, has often been criticised for its treatment of migrants.
On Tuesday, parliament approved plans to confine all new asylum-seekers, as well as those already in Hungary, in container camps at its southern border while their applications are processed -- unless they choose to return to Serbia.
The legislation, which was sharply criticised by the UN's refugee agency (UNHCR) and others, is aimed at keeping Hungary and Europe safer, Orban said on Tuesday.
Immigration, he said, was "the Trojan Horse of terrorism".
The Council of Europe also voiced its concerns on Wednesday.
"Automatically depriving all asylum seekers of their liberty would be in clear violation of Hungary's obligations under the European Convention on Human Rights," it said.
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