Young demonstrators clashed with police on Thursday night.
Kuwait vowed at the weekend to take all necessary measures against "any signs of disturbance and violence" after police dispersed demonstrators the Gulf Arab state said had thrown stones, burned car tyres and blocked roads.
Dozens of men staged a march on Thursday night to demand the release of prominent politician Musallam Al Barrak, who has been detained for questioning over allegedly insulting the judiciary, Kuwaiti media reported. A court hearing for Barrak, a former opposition lawmaker, has been set for Monday.
"A crowd and troublemakers organised an unauthorised assembly last night violating the laws that ban such marches," Kuwait's Interior Ministry said in a statement carried by state news agency KUNA.
"Despite the attempts of the security men to urge the crowd to give up their illegal and irresponsible acts, they continued to gather and blocked the main roads and threw rocks at the security men."
"The Interior Ministry will firmly confront any signs of disturbance, violence and incitement ... to prevent them harming the security and safety of the nation and of citizens."
The mostly young demonstrators set fire to tyres and garbage containers and destroyed a restaurant, the ministry said, adding that 13 people had been arrested.
The Alaan news website showed pictures of injured protesters and said police had used a water cannon and tear gas to disperse the crowds. Kuwaiti newspaper al-Rai said police had used tear gas and stun grenades to break up another rally on Wednesday.
OPEC producer Kuwait, a U.S. ally, allows more political freedom than other Gulf Arab states. It has a lively press and an elected parliament, but it has also banned public gatherings of more than 20 people without a permit.
Unrest flared in Kuwait in 2012 after the ruling emir, Sheikh Sabah Al Ahmed Al Sabah, changed the electoral law before a parliamentary election in December that year.
Barrak and other opposition groups said the move had been intended to deny them a majority and they boycotted the poll.
Barrak, who draws support from some of Kuwait's powerful tribes, was sentenced to jail for insulting the emir in 2013. His arrest and conviction triggered a series of street protests. He was later acquitted.