Woodhead was carted off the field after hurting his right ankle early in the first quarter against the Buffalo Bills on Sunday.
Chargers head coach Mike McCoy had no update on Woodhead's ankle injury after the game. He said the team will run more tests Sunday night and provide more info Monday.
Woodhead was hurt on a 1-yard run, when he was stopped by diving defensive tackle Kyle Williams. Williams hit Woodhead directly in the right ankle, which appeared to twist underneath the player.
Woodhead was briefly treated on the field before being loaded into a cart.
The Chargers were already thin at running back heading into the contest, with Ryan Mathews out for four to five weeks with an MCL knee sprain. San Diego has just two healthy running backs on the active roster in Donald Brown and rookie Branden Oliver. The Chargers also have rookie Marion Grice available on the team's practice squad.
"Unfortunately, that's the nature of the sport, said Brown, who finished with 62 yards on 31 carries in San Diego's 22-10 win at Buffalo. "Guys are going to get hurt, and other guys have to step out and carry the load. Next man (up) is pretty much the mantra of this team."
With Woodhead and Mathews likely out for an extended period, San Diego's running back depth will be tested.
"Hey, we're going to keep rolling," McCoy said, when asked about running back depth. "We have to keep going, and we're not going to make any excuses."