African Union (AU) troops raped women and girls seeking medical aid or water from their base in Somalia's capital, Mogadishu, a rights group said.
The troops had "misused" their power over women fleeing violence and poverty, Human Rights Watch (HRW) said, BBC reported.
One Muslim girl, aged 15, reportedly had her headscarf ripped off before being raped.
The AU, which has some 22,000 troops fighting extremist militants in Somalia, has not yet commented on the report.
Last year, it faced protests by women activists following claims that AU and government soldiers had gang-raped a woman.
The AU promised to investigate the incident and to take steps to "enhance the security of women".
Most of the women who were abused lived in camps for displaced people after fleeing violence and the 2011 famine, HRW said.
"The AU can no longer turn a blind eye to the abuses on Amisom )AU Mission in Somalia( bases, as it's undermining the very credibility of the mission," said Liesl Gerntholtz, HRW's women's rights director.
It interviewed 21 women and girls who described being raped or sexually exploited by Ugandan or Burundian soldiers in the AU force, HRW said.
Only one rape case, in which the victim was a child, is before Uganda's military court in Kampala, it said.
Somalia has been hit by instability since the overthrow of long-serving ruler Siad Barre in 1991.