The television on Sunday carried an official statement from the royal court announcing the amir’s death.
The amir was the 13th ruler of a 245-year-old dynasty which 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 US calls for change in the Middle East, the ruling family had come under intense pressure from both Islamists and pro-Western liberals to loosen its grip on the government and share power.
Kuwait, a founder member of the OPEC and a key US ally, 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 Gulf state sits on one tenth of the world's crude oil reserves, or 95 billion barrels.
Used as the main launch pad for the US-led invasion of Iraq in 2003, Kuwait hosts up to 30,000 US troops; besides, 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.