The aid was being unloaded from a Colombian ship at the port in Dame-Marie when a stampede occurred.
The much-needed aid was being unloaded from a Colombian ship at the port in the southwestern town of Dame-Marie when a stampede occurred on the dock in the afternoon.
"The Brazilian peacekeepers who were there supporting the Haitian national police fired rubber bullets and two tear-gas grenades," Mourad Wahba, the UN humanitarian coordinator in Haiti, told AFP.
National police fired live ammunition at the crowd demonstrating over the slow pace of aid some three weeks after Hurricane Matthew struck southern Haiti, killing at least 546 people and leaving 175,000 without homes.
The girl who died was struck in the chest by a bullet and three other victims suffered gunshot wounds, Wahba said, adding that a UN investigation was under way.
The exact circumstances surrounding the death, however, were not immediately clear.
A spokesman for Haiti's national police said he was unable to confirm details surrounding the fatality.
UN Secretary-General Ban Ki-moon has recently voiced distress and disappointment at scant emergency aid reaching the struggling nation.