HRW said in a report published on Monday that it documented 43 cases of women and girls in seven internally displaced persons' camps in Maiduguri, the epicentre of a seven-year battle with Boko Haram, who had been abused by camp leaders, policemen and soldiers.
"It is bad enough that these women and girls are not getting much-needed support for the horrific trauma they suffered at the hands of Boko Haram," said Mausi Segun, senior Nigeria researcher at HRW.
"It is disgraceful and outrageous that people who should protect these women and girls are attacking and abusing them," she added.
Nigerian President Muhammadu Buhari said in a statement that he was "worried and shocked" by the report and directed police to "immediately commence investigations into the issue".
"The welfare of these most vulnerable of Nigerian citizens has been a priority of his government," presidency spokesman Garba Shehu said, adding that the allegations raised by the HRW "are not being taken lightly".
Four of the victims told HRW they were drugged and raped, while 37 were coerced into sex through false marriage promises and material and financial assistance.
"Many of those coerced into sex said they were abandoned if they became pregnant. They and their children have suffered discrimination, abuse, and stigmatisation from other camp residents," the global rights body said.
HRW spoke to one 17-year-old girl who was raped and made pregnant by a policeman.
"One day he demanded to have sex with me," she said. "I refused but he forced me. It happened just that one time, but soon I realised I was pregnant.
"When I informed him about my condition, he threatened to shoot and kill me if I told anyone else. So I was too afraid to report him."
HRW said irregular supplies of food, clothing, medicine and other essentials in camps were making the women vulnerable to abuse and exploitation.
"In some cases, men used their positions of authority and gifts of desperately needed food or other items to have sex with women," it said.
Boko Haram has devastated northeast Nigeria, killing more than 20,000 people and displacing 2.6 million from their homes. Since taking up arms against the Nigerian government in 2009, the group has also disrupted trade routes and farms.
Now, nearly 50,000 children face death by starvation if they don't get food and almost 250,000 more are severely malnourished in Borno state, according to UNICEF.