The COVID-19 list was created this summer for a player who either tests positive for or who has been quarantined after having been in close contact with an infected person or persons.
Players will remain on the list until they are medically cleared to return.
Minshew, 24, is a former sixth-round pick of the Jaguars out of Washington State back in 2019. He signed a four-year rookie deal worth $2.7 million and will make a base salary of 585,000 for the 2020 season.
In 2019, Minshew appeared in 14 games for the Jaguars and completed 60.6 percent of his passes for 3,271 yards, 21 touchdowns and six interceptions. He also rushed for 344 yards.