The ban, announced on Thursday, has exacerbated tensions in a country still divided despite the official end of a civil war.
The violence highlighted simmering instability in the world's top cocoa producer, despite a peace deal meant to end a civil war triggered by a failed coup last year.
Government spokesman Adjoumani Kobenan said all public demonstrations were suspended for a period of three months.
"Over the past week, spontaneous demonstrations of unprecedented violence and a nameless barbarism have been organised in different parts of Abidjan," he said after a weekly government meeting.
Kobenan said the government had also decided to pursue those responsible for the damage caused during last week's riot.
Pro-government militiamen dressed in combat gear and carrying iron bars and clubs smashed offices and looted goods in Abidjan, especially targeting businesses owned by citizens of former colonial power France.
They accuse some of the 4000 French troops policing a ceasefire line of helping rebels who control half the country.
"Over the past week, spontaneous demonstrations of unprecedented violence and a nameless barbarism have been organised in different parts of Abidjan"
Fighting in Ivory Coast has stopped since the May ceasefire but rebel forces still control the mainly Muslim northern half.
Last month, ministers from the rebel New Forces pulled out of a power-sharing government, accusing President Laurent Gbagbo of undermining a peace accord brokered by France.
They recently said they would only return if Gbagbo quit.
On Thursday, the New Forces condemned the decision to ban all marches, saying it was "a step backwards for democracy which violated constitutional liberties". It said in a statement that people would be allowed to demonstrate in the zones it controls.
Kobenan also announced the dissolution of a notorious pro-government militia, that has repeatedly threatened to take up arms to defend Gbagbo.
He said members of the militia were guilty of forgery, with some carrying professional cards resembling those given to the defence and security forces.