Whether the right fielder eventually ends up on the shelf depends on how his ailing left thumb responds to treatment.
"That's just day to day right now," general manager Kevin Towers said.
Upton was out of the starting lineup on Wednesday for the second straight game, but he did appear as a pinch-runner in the ninth.
Upton injured the thumb when he jammed it sliding into second base during the April 8 game against the Giants. An MRI was performed, and fluid was drained from the thumb on Tuesday night.
"[It's] probably a little bit better today, hopefully [it will be] a little bit better tomorrow," Towers said. "Hopefully, he'll be able to avoid the DL. If not, we'll have to deal with that, too. Hopefully, he'll be fine the next two or three days, and we'll be able to get him back in the lineup."
Though Upton had played through the injury without complaint up until the last couple of days, it clearly was affecting him at the plate, as he is hitting just .212 with two doubles and no homers.