Four fighters were killed, three arrested and three wounded in al-Qurain region south of Kuwait City. Three security men were also injured, ministry spokesman Adil al-Hashshash told state television on Monday.
The fighting ended after the surrender of three accused insurgents, including key suspect Amir Khulaif al-Anaizy, the spokesman added.
Kuwait TV reported that a civilian was also killed. The operation was "a spectacular success", he said.
"The neighbourhood has been cordoned off completely by hundreds of police including commandos, and shots seem to be concentrated at one villa," one witness said early on Monday.
Kuwait has been experiencing a surge of politically motivated violence, believed to be linked to al-Qaida.
On Sunday, an insurgent, a policeman and a Bahraini bystander were killed in a gun battle in al-Salimiya district.
The US, British and French embassies in Kuwait have advised their nationals to avoid certain areas in the country, and warned of the danger of more unrest.
Since 2002, fighters have carried out several attacks against Americans in Kuwait, killing one US marine and a civilian contracted to the US military.