He was expected to be succeeded by his 83-year-old half-brother and crown prince, Sheikh Nawaf al-Ahmed, reports BBC quoting the state media.
In July, Sheikh Sabah was flown to the United States for medical treatment following surgery for an unspecified condition in Kuwait.
He had ruled the oil-rich Gulf Arab state since 2006 after Emir Sheikh Saad al-Abdullah stepped down just nine days into his rule as parliament moved to depose him on health grounds.
The emir often acted as a mediator in regional disputes, including the ongoing diplomatic stand-off between Saudi Arabia, its allies and Qatar.
Kuwait also refrained from intervening in Syria's civil war, instead hosting several donor conferences for humanitarian aid.
He had been prime minister under the previous Emir, Sheikh Jaber al-Ahmad al-Jaber al-Sabah, and for several years had been seen as the de facto ruler.
Before then, he served as foreign minister from 1963 to 1991 and from 1992 to 2003.
Kuwait - which has a population of 4.8 million, including 3.4 million foreigners - has the world's sixth-largest known oil reserves and is a major US ally.
It has been ruled by the Sabah family for the past 260 years.
Sheikh Sabah had pushed for diplomacy to solve regional issues, such as the continuing boycott of Qatar by four Arab nations, and he hosted major donor conferences for war-torn nations such as Iraq and Syria, reported Al Jazeera.
Kuwait television earlier interrupted regular programming to cut to Quaranic verses on Tuesday, a move that often signifies the death of a senior member of the Gulf Arab state’s ruling family.
His death comes as the nation continues to fight the coronavirus pandemic, which has infected more than 103,981 people and caused 605 related deaths in the country of 4.1 million. Its health ministry said more than 95,500 people have recovered from COVID-19.
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