Schwartz went to the locker room after sustaining the ailment in the first quarter and didn't return to the contest.
Chiefs head coach Andy Reid said after the game that Schwartz's back "was bothering him," according to Nate Taylor of The Athletic.
Kansas City listed Schwartz as questionable prior to Week 6 due to a back injury but eventually gave the veteran blocker the green light to face the Bills.
Entering Monday, the 31-year-old had yet to miss an offensive snap this season.
The four-time All-Pro has started every game for the Chiefs since they drafted him in the second round in 2012.
Kansas City defensive end Alex Okafor also missed most of Monday's contest due to a hamstring injury.