One of the five arrested is believed to be the ringleader of the Monday riots, which caused about $7.4 million worth of damage to public buildings and left 16 police officers injured, Radio France Internationale reported.
The suspected ringleader has been charged with incitement to rebellion, which is punishable by a 10-year prison term if the perpetrator was armed at the time the riot.
Amiens residents said the riots came after years of police harassment of youth in a neighborhood where two out of three people are under 25 and out of work.
Two of those arrested Thursday were minors.
Police said they identified the suspects through thermal images taken from a helicopter during the riots, adding that they waited to make the arrests over fear of further agitating an already tense situation.
"The investigation is ongoing" said a police spokesperson, adding "these are only the first arrests."