Abbasi, along with another internationally-known Iranian Qari, Hamid Shakernejad, had been seriously injured in a car accident last week.
The accident happened when they were on their way to Mashhad returning from a trip to the central city of Semnan to serve as arbiters in a Quran competition there.
Born in 1976 in Zanjan, west of Tehran, Abbasi won a number of titles in international Quran competitions, including those in Kuwait and Malaysia.
He was an honorary Quran reciter at the holy mausoleum of Imam Reza (AS) in Mashhad.