Reliever Evan Marshall was removed from Monday's game in the eighth inning with right elbow soreness.
"The way he termed it, he flicked the nerve in his elbow. Those were his words. We'll know a lot more (Tuesday)," Indians manager Terry Francona said.
It's possible Marshall may have to be placed on the disabled list on Tuesday, which means the Indians would have to recall another reliever from Triple-A Columbus.
On Sunday, the Indians placed starter Carlos Carrasco on the 10-day disabled list with a right elbow contusion. The Indians on Monday also signed left-handed reliever Marc Rzepczynski to a minor league contract, with an eye toward eventually adding him to their banged-up bullpen.
With a 6-2 win Monday in the first game of the series, Cleveland is 6-2 this year against the White Sox, who go into Tuesday's game with a five-game losing streak. The White Sox (24-47) are a season-worst 23 games below .500.
The pitching matchup Tuesday night will be identical to the one when the same two teams faced each other on Thursday in Chicago: White Sox left-hander Carlos Rodon vs. Indians right-hander Mike Clevinger.
In that game in Chicago last week, the White Sox won 5-2, although Rodon (0-1, 3.60) did not figure in the decision. He pitched five innings, giving up two runs on two hits, with four strikeouts and three walks, throwing 100 pitches.
"I don't want to make that excuse. When you show up at this level, it's time to compete," Rodon told reporters, "A little inconsistent today. A little everywhere. Try to get that back on track. Fastballs in, that's the key for me. I have a good fastball, just have to throw it."
Clevinger (5-2, 3.15) took the loss but he pitched well, working seven innings, giving up one earned run on five hits, with 11 strikeouts and one walk. He threw 99 pitches.
Last year, Rodon started one game against the Indians, a 3-1 Chicago win on July 30 in which Rodon did not get a decision. He pitched 6 2/3 innings, allowing one run on six hits, with nine strikeouts and two walks. In 11 career appearances against Cleveland Rodon is 4-1 with a 2.43 ERA.
Clevinger has pitched well lately.
In his last four starts he is 2-0 with a 1.32 ERA and an opponents' batting average of .206. In six career appearances against the White Sox he is 2-2 with a 3.54 ERA.
The Indians did get some good news Monday on Carrasco, who left Saturday's game against the Twins in the second inning after getting hit in the right elbow by a line drive. An MRI done on Carrasco's elbow Monday showed no serious damage.
"Everything came back negative. We dodged a huge bullet," Francona said. "They are treating it as a contusion. Once we get the swelling down the hope is he'll come back quick. It's just a bruise."
The Indians on Monday also activated first baseman Yonder Alonso off the Family Medical Emergency List, and they optioned outfielder Greg Allen to Triple-A Columbus.
With left-handed relievers Andrew Miller and Tyler Olson on the disabled list, the Indians signed Rzepczynski to a minor league contract and assigned him to Columbus. Rzepczynski, who pitched for the Indians from 2013-15, was designated for assignment by Seattle on June 1.
"He's a guy we know and like, and he enjoyed his time here," Francona said. "He'll start pitching (Tuesday). We're down one left-hander in the pen now, so he's a guy who could help."