Hannibal Qaddafi began the strike on June 3 in protest against his detention without trial, which began in 2015.
He was transferred to the Hotel-Dieu de France hospital on Sunday due to low blood sugar levels, his lawyer Paul Romanos has said.
While some reports said Mr Qaddafi was in “critical condition,” Mr Romanos said his client was “stable”.
Mr Al Sadr is a highly revered figure in the Shiite community and founded the powerful Lebanese movement Amal, now headed by influential Parliament Speaker Nabih Berri. Images of both men adorn the streets of Shiite-dominated neighbourhoods of Lebanon.
Muammar Qaddafi was captured and killed by rebels in 2011 during the Libyan Civil War – an uprising against his 42-year rule.
Hannibal Qaddafi was only aged two at the time of Mr Al Sadr’s disappearance. He has maintained his innocence and said he is a victim of injustice.
Hannibal Qaddafi fled Libya in 2011 as the uprising spread.
He was detained by an armed group in Lebanon in 2015, and handed over to authorities.
Mr Sadr, who Libya said left the country safely in 1978, is widely believed to have been killed shortly after his disappearance.
The Amal Movement and its ally Hezbollah dominate Shiite politics in Lebanon.
The latter is a heavily armed Iran-backed political party and militia, which holds significant sway in Lebanon.
Hannibal Qaddafi had several siblings, some more prominent than others. Seif Al Islam Qaddafi, who is wanted for crimes against humanity by the International Criminal Court, was his father’s heir apparent. He remains in Libya in an undisclosed location near the town of Zintan and has made no secret of harbouring leadership desires.
Saadi Qaddafi, a retired professional footballer, was released from detention in the Libyan capital of Tripoli in 2021 and is now believed to be in Turkey.
Source: The National News