The governor said the curfew will run from midnight to 5 a.m.
"This is a test, the eyes of the world are watching," Nixon said. "This is a test to see if this community can break the cycle of violence and replace it with peace."
The announcement comes after looters broke into a number of stores overnight, and threw rocks and other objects at police.
On Friday, police had released the name of the officer who fatally shot 18-year-old Michael Brown, and also alleged that Brown robbed a store before he died.
The governor and Missouri Highway Patrol Capt. Ronald Johnson, who was put in charge of policing the St. Louis suburb this week, said they were trying to find a balance between allowing the peaceful demonstrations to continue, but to stop the looting and other disturbances that have occurred many nights since the shooting a week ago.
Both men were interrupted repeatedly by members of the emotional audience, but they seemed determined to let people voice their frustration with how police have handled the investigation into Brown's death.