Francona told reporters Tuesday that the starting pitcher was headed to the injured list due to the non-displaced fracture of his right thumb. He sustained the injury after the Indians' 8-5 loss to the Minnesota Twins on Sunday in Cleveland.
Plesac caught the thumb on a chair when he took off his undershirt.
"He was, I think, probably rather aggressively ripping off his shirt," Francona said. "He called [athletic trainer] James Quinlan, and James called me. It was pretty swollen [Monday]. ... As you can imagine, our wheels started to turn."
Plesac underwent an X-ray on Monday and will meet with Dr. Thomas Graham on Wednesday in Dayton, Ohio.
He is 4-3 with a 4.14 ERA in 10 starts this season.
The Indians face the Detroit Tigers in the third game of a four-game series at 7:10 p.m. EDT Wednesday at Comerica Park in Detroit. Right-handed pitcher Triston McKenzie is expected to start for the Indians. Jose Urena is expected to pitch for the Tigers.