The Libyan Antonov aircraft went down after the pilot tried to land in farmland near Grombalia, south of Tunis.
Sheikh Meftah Daouadi, undersecretary at the Libyan Ministry of Martyrs which looks after families of fighters killed in Libya's 2011 revolution, was among the dead.
The veteran Islamist fighter took part in the revolt against Libyan leader Muammar Gaddafi. It was unclear whether he was a patient, or was on the plane accompanying one of the other passengers.
Six crew members, as well as the patients and their companions, died.
Patients from Libya often travel to Tunisia for medical treatment.
It was the second crash involving a military plane in North Africa in two weeks after an Algerian military transport plane crashed into a mountain in bad weather on February 11, killing 77 people, the country's worst air disaster in a decade.