Students have also led protests against the elimination of some classes from school curriculum and demanded an increase in Haiti's minimum wage.
The violence comes just days before elections in the country.
Following the shooting, some mourners began smashing the windows of cars and buildings, the Associated Press news agency reported.
The demonstrators later took the victim's body from the scene and planned to lay it down in front of the presidential palace, but a police ambulance intervened and took the body to the city's morgue, the Reuters news agency reported.
'Shot in the air'
Sophie Boutaud De La Combe, a spokeswoman for the UN mission in Haiti, said UN soldiers shot in the air to deter protesters who were throwing rocks at them.
She did not rule out that gunshots fired by UN troops could have hit the victim, but said they would have to await the results of a ballistics test and autopsy.
Jean-Juste was arrested in 2005 on suspicion of playing a role in the kidnapping and slaying of a prominent Haitian journalist but he denied involvement and human rights groups said the charges were politically motivated.
He was released in 2006 following intense international pressure, particularly from US politicians, and all the charges against him were dropped.