The closed areas in the northern and western parts of the country make up about one third of its territory.
Despite the hightened security, there has been another shooting incident involving American forces.
A US military spokesman said shots were fired in the vicinity of troops training south of Kuwait City.
No one was hurt and the Americans did not return fire.
Camps dismantled
The Kuwaiti authorities say the decision to seal off a large part of the country is not linked to US preparations for a possible war in Iraq.
"This is an area for exercises...and the ban will be lifted when the war games end," Defence Minister Sheikh Jaber al-Hamad al-Sabah said.
Scores of desert camps were dismantled on Friday and moved out of areas in north and west Kuwait.
The BBC's Paul Harper, reporting from Kuwait, says recent attacks on American soldiers, in the most serious of which a marine was shot dead, have been blamed on al-Qaeda.
They are especially worrying for the US authorities because they have been pouring troops and equipment into the country, which would serve as one of the main staging posts in the event of a war with Iraq.
Since Kuwait's liberation from Iraqi occupation over a decade ago, it has been America's staunchest ally in the Gulf.
But these attacks suggest it is no longer immune to the anti-American sentiments which are widespread in the rest of the Arab world.
Pick-up trucks
Details of the latest shooting incident are sketchy, but the spokesman is quoted as saying that the troops involved believe the shots were fired from two white pick-up trucks with two people in each of them.
It is the fourth such incident in less than a month.
Kuwaiti police are said to have detained four people.
But the authorities dismissed the latest incident.
"We do not think it is anything significant or terrorism," a senior Kuwaiti official said.