This is the first player of the week award for Johnson in his four-year career and the first for a Bengals defensive lineman since Antwan Odom in 2009.
Johnson's constant pressure on rookie quarterback Robert Griffin III helped hold the Redskins to 168 passing yards and a 25 percent conversion rate on third downs.
Johnson is second in the AFC with four sacks this season. The Bengals' defense ranks first in the conference with 11 sacks.
He is also the first AFC North player this season to win the defensive player of the week award. Ravens quarterback Joe Flacco (offensive player in Week 1) and Bengals punt returner Adam Jones (special teams player in Week 2) have previously been recognized this season.