The ayatollah, in his late 70s, was stripped of his Bahraini nationality in 2016 on charges of "serving foreign interests".
He flew out of the country at 10:30 AM (0730 GMT) using a temporary passport -- valid for one year , the aides said.
While the family has not made public the details of his condition, rights groups say the cleric has high blood pressure, diabetes and heart disease.
The cleric's health has for months been a point of contention between authorities and his family, who had refused offers to transfer him to hospital over fears he could be detained and deported.
He did however undergo surgery in December before returning to de facto house arrest, activists said.
In January, a Bahraini court upheld the decision to revoke his nationality.
Those close to Ayatollah Qassim, who has played a leading role in protests against Bahrain's monarchy, said the issue of payment had not yet been decided.
Sheikh Ali Salman, head of Bahrain's largest -- and now banned -- Shiite opposition group Al-Wefaq was found not guilty on charges of spying for regional rival Qatar.
Security forces crushed demonstrations demanding a constitutional monarchy and an elected prime minister in 2011.
Authorities have jailed dozens of high-profile activists, disbanded opposition groups and stripped hundreds of people of their citizenship.