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The statement announced a 40-day mourning.
Government offices will be closed for three days.
Sheikh Jaber, who ruled since 1978, had been ill since suffering a brain hemorrhage in September 2001.
State television broadcast verses of the Koran after the announcement.
The emir was the 13th ruler of a 245-year-old dynasty that has ruled Kuwait since the Anaiza tribe, to which the al-Sabahs belonged, migrated from the Arabian hinterland.
Since the fall of Saddam Hussein in neighbouring Iraq in 2003 and United States calls for change in the Middle East, the ruling family had come under intense pressure from Islamists and pro-Western liberals to loosen its grip on the government and share power.
Kuwait, a founder OPEC member, enjoys one of the world's highest standards of living, despite its reliance on oil exports, unpredictable oil income and huge losses from the 1990-1991 Iraq occupation.
The small Gulf state sits on one-tenth of the world's crude oil reserves, or 95 billion barrels.
Used as the launchpad for the US-led invasion of Iraq in 2003, Kuwait hosts up to 30,000 US troops and some 13,000 US citizens live in the country.
Kuwait has cracked down on Islamists opposing the US military presence there.
Diplomats say radical Islam is taking hold among Kuwaiti youth.
In December, a Kuwaiti court sentenced to death six suspected militants linked to Al Qaeda for bloody attacks in the country.
The six were among 37 Islamists on trial as members of the Peninsula Lions group believed to be linked to Osama bin Laden's Al Qaeda in Iraq and Saudi Arabia.
-(DILIGENT MEDIA CORP. article)