Twelve inmates at a medium-security prison in the southern city of Foggia died of drug overdoses after they broke into the prison infirmary during the riots, which began Sunday.
Eleven other inmates who escaped during the riots remain on the lam.
The riots were touched off after Italian corrections officials announced they were suspending or limiting family visits to more than two dozen prisons for the next two weeks, due to coronavirus concerns.
The affected prisons house a total of more than 6,000 inmates.
"It's evident that so many prisoners are worried, especially in overcrowded conditions, about the impact of coronavirus on inmates' health," Justice Minister Alfonso Bonafede said according to the Agence France-Presse.
Bonafede told the Italian Senate on Wednesday that about 100,000 protective masks were being distributed throughout the prison system, while tests for coronavirus would soon be conducted on inmates who had recently been transferred between institutions.
As of Wednesday afternoon, there were more than 12,400 confirmed COVID-19 cases and more than 800 fatalities in Italy, according to Italy's Civil Protective Agency.
The country has the highest death toll related to the novel coronavirus outside of Wuhan, China, where the virus originated.