The rookie linebacker made his NFL debut in the team's 31-10 defeat to the Seattle Seahawks earlier this week.
Head coach Mike McCoy confirmed the injury in a press conference, telling reporters: "Manti has a foot sprain and he'll be out this week. I'll give you further updates as the week goes along or next week sometime, but he'll be out for the week.
"We diagnosed it after the game. I think any player is a little disappointed when they have a little injury that will keep them out for a little bit. But it's part of the game and he'll do whatever he can to get back on the field as quickly as possible."
Te'o, who was a finallist for last year's Heisman Trophy, was selected by the Chargers in the second round of this year's draft.