"There was an explosion this morning and the info I have is that there were several dead and wounded among the blue helmets," Fred Fath, the mission spokesman, told The Associated Press.
An intelligence official in northern Mali said that the dead included two Senegalese peacekeepers. He spoke anonymously because he was not authorised to speak to the media.
The car packed with explosives detonated in front of a bank guarded by the peacekeepers, he said. The explosion was so great it blew open the doors of houses in the area.
Kidal, located some 1600 kilometres (1000 miles) northeast of Mali's capital, is where an ethnic Tuareg rebellion began in late 2011.
The French military deployed to Mali in January succeeded in chasing the rebels from almost all the areas they controlled, except Kidal which remains the nucleus of the conflict.