Abdel-Basset Ben Mberek, the lawyer, said his client died Thursday after being transferred to a Tunis hospital when his condition declined.
Bachir al-Gholi, 23 and father of a six-month-old daughter, survived two heart attacks and succumbed to the third, his lawyer added.
Following region-wide anger over a U.S.-made film insulting the Prophet Muhammad, some 2,000 militants attacked the U.S. embassy in Tunis in September and looted a nearby school.
According to the Justice Ministry, some 123 people have been arrested in the ongoing investigation.
Al-Gholi's lawyer said his client maintained his innocence.