Mohamed Ag Intalla, a Kidal traditional chief and national assembly member, said the wounded have been hospitalized.
Protester Mohamed Ag Ibrahim said dozens of demonstrators set fire to a firefighting car and generators to protest against French forces for extraditing recently arrested people to Gao and Bamako.
The United Nations Mali mission said demonstrators broke into the airport, a key center for humanitarian assistance in northern Mali.
The UN said peacekeepers have left the airstrip and returned to their base in Kidal.