The reported cases took place in 2014 but came to light only in recent weeks.
The alleged abuse involved six children: five girls and a boy who were between the ages of 7 and 16 at the time it is said to have taken place.
The soldiers are believed to be from Georgia, France and the European Union.
"These are extremely serious accusations and it is crucial that these cases are thoroughly and urgently investigated," Zeid Ra'ad Al Hussein, the U.N. high commissioner for human rights, said Friday.
"I am heartened at the initial responses we have received from the countries concerned, as well as from the European Union, which show they take these terrible allegations very seriously."
All six cases took place in or near the M'Poko camp for displaced people next to the airport in the capital, Bangui.
Not the first time
In August, three females, including a minor, accused U.N. peacekeepers working in the Central African Republic of rape, a spokeswoman said at the time.
Their families reported the alleged abuse to the U.N. mission there, spokeswoman Vannina Maestracci told reporters. It was not immediately clear how many troops were allegedly involved.
News of the August allegations came a week after the head of the U.N. peacekeepers in the Central African Republic was fired over previous sex abuse accusations.
"I believe the disturbing number of allegations we have seen in many countries -- but particularly in the Central African Republic in the period before U.N. peacekeepers were deployed and since -- speaks to the need to take action now," U.N. Secretary-General Ban Ki-moon said in August. "Enough is enough."
There have been 14 allegations of sexual exploitation and abuse by U.N. peacekeepers in the Central African Republic
since the United Nations established a force there in April 2014.
Similar allegations also were made against French peacekeepers who arrived in the country a year before the U.N. force.
Peacekeepers' involvement in the Central African Republic, one of the world's poorest nations, stems from political violence that began in 2013.
France and African nations sent peacekeepers after a coalition of mostly Muslim rebels ousted President Francois Bozize in March 2013. Christian and Muslim militias battled for control before a tentative political transition began.
The violence prompted a humanitarian crisis, with hundreds of thousands of people fleeing their homes. Some sought refuge in neighboring countries, but many others were internally displaced, living in makeshift camps.