Bosa finished the game with a team-high seven tackles and a sack in the 49ers' 9-0 win over Washington.
The other award nominees are Jacksonville Jaguars quarterback Gardner Minshew, Oakland Raiders running back Josh Jacobs, Los Angeles Chargers safety Roderic Teamer, and Tennessee Titans defensive lineman Jeffery Simmons.
Minshew ended up winning the award following Week 5, which was the last time (and the first time) Bosa was nominated. Minshew has already won the Pepsi NFL Rookie of the Week Award four times this season.
Fans can click here to vote for the 49ers rookie through Friday. Bosa played college football at Ohio State, and the 49ers made him the No. 2 overall pick in April.