Per ESPN.com's Adam Schefter, Bosa is dealing with a bruised bone in his left foot and isn't expected to return until October.
The Chargers had already ruled Bosa out for their Week 2 game against the Buffalo Bills.
Schefter noted the team is hoping swelling goes down in Bosa's foot with rehab, but surgery could be an option. He originally injured his foot during practice in August.
At Chargers practice Sept. 7, Bosa was seen wearing a walking boot on his left foot.
Head coach Anthony Lynn told SiriusXM NFL Radio on Thursday that Bosa was officially considered week-to-week.
Now in his third NFL season, Bosa has been one of the NFL's top pass-rushers since his debut. The 23-year-old has 23 sacks and five forced fumbles in 28 career games.