"We'll probably know more on Monday," White Sox manager Rick Renteria said. "Felt better this morning, but for us, once we took him out, just take him back [to Chicago], be precautionary. He'll be re-evaluated to see where he's at.
"Once he gets seen on Monday, we'll know where he's at."
Delmonico hit .262 with nine home runs, 23 RBIs and an .856 OPS during an effective rookie season with the White Sox.
Catcher Omar Narvaez did not make the trip with the White Sox to Cleveland. He had been bothered by right elbow soreness and received PRP (platelet-rich plasma) injections.
Anderson gets day off
Tim Anderson knew about his day off Saturday before he arrived at Progressive Field. White Sox first baseman Jose Abreu also knew Anderson was sitting, humorously taping up the shortstop's locker and putting a sign reading "Off" on the tape.
Anderson tweeted a picture with the hashtag #thanksAbreu, adding it took him five minutes to get rid of all the tape.
"It was very funny, though," Anderson said. "Good day to have off, I guess. It's been a long season."
Anderson has played 145 games and has a career-high 17 home runs, 56 RBIs and 26 doubles.
"I'm kind of feeling it in my body," said Anderson, who played 99 games for the White Sox during his rookie season in 2016. "First time I've played this many games. Something I've got to definitely get used to so I can play some more in October."
Scott Merkin has covered the White Sox for MLB.com since 2003. Read his blog, Merk's Works, follow him on Twitter @scottmerkin, on Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.