The refugees "speak of children dying of hunger and digging new graves every day," according to a statement from the global medical charity group, also known by its French acronym MSF.
"A catastrophic humanitarian emergency" is unfolding at a makeshift camp on a hospital compound where 24,000 people have taken refuge, it said.
The doctors referred 16 emaciated children at risk of dying to their special feeding centre in Maiduguri. One in five of the 15,000 children are suffering severe acute malnutrition, the group found.
"We see the trauma on the faces of our patients who have witnessed and survived many horrors," said Ghada Hatim, head of the Doctors Without Borders mission in Nigeria.
Her team reached Bama on Tuesday following a military convoy from Maiduguri, the Borno state capital that is the headquarters of Nigeria's military campaign.
Though Bama is just 70km southeast of Maiduguri, ongoing clashes between the rebels and government troops make travel unsafe and farmers have not planted crops for 18 months, Dr Christopher Mampula of MSF explained by telephone from Paris.
Boko Haram fighters routinely burn down homes and destroy wells, leaving few water sources in an area where temperatures often soar above 40 degrees.
The armed group seized Bama in September 2014 and Nigerian troops recaptured it in March 2015.
Nigeria's military has greatly curtailed the seven-year-old armed rebellion that has killed some 20,000 people, but fighters still attack villages and deploy suicide bombers.
Boko Haram has also staged attacks across Nigeria's borders in Chad, Niger and Cameroon.
The refugees in Bama are among 1.8 million Nigerians forced from their homes and living inside the country, with another 155,000 in neighbouring countries, according to the UN.