Davis was trying to beat out a slow ground ball and came down on the front edge of the bag. He limped off the field and was replaced at first base by Ryan Flaherty.
Interviewed on MASN, manager Buck Showalter said Davis is "pretty upbeat about it," which is a good sign.
"We'll see what we've got," Showalter said. "It just bit him there on that last step. And as Chris does, he plays the game hard. He almost beat it out. We're hoping for good news and we'll see."
Showalter mentioned Flaherty, Steve Pearce and Nick Markakis as being capable of playing first base in Davis' absence. He also brought up Matt Wieters' name, but the Orioles would much prefer to keep him behind the plate.
Miguel Gonzalez's next start is in jeopardy because of a blister on his right thumb that forced him out of the game after six innings and 80 pitches.
The Orioles are off Monday, so they could tweak the rotation and give Gonzalez's thumb additional time to heal.
"He ripped a blister off that last inning. He got it pretty deep," Showalter said on MASN. "That's going to be a challenge for him. We've got an off day and we'll see whether he's going to be able to make his next start. That's a pretty deep blister."