Troy A. Ashmus, 58, died on Monday at an outside hospital. He is the 13th inmate to die at the prison since the outbreak began and the seventh on death row.
Ashmus was sentenced to death in 1986 for first-degree murder and other charges related to the assault and death of a child.
More than 900 inmates at San Quentin are still sick with active cases of COVID-19.
The outbreak has infected nearly 60% of the inmate population and more than 200 employees, but appears to be slowing.