Tomlin had been scheduled to start Saturday night's game against Boston, but was scratched earlier in the day before the Indians placed him on the DL, retroactive to May 8. He is eligible to come off May 23.
Zach McAllister was recalled from Triple-A Columbus to replace Tomlin. Earlier this week, McAllister recorded his first major league win against Chicago in the opener of a day-night doubleheader.
McAllister allowed two earned runs and six hits in a career-high six innings.
The team has designated outfielder Nick Weglarz for assignment.
Tomlin is 1-2 with a 4.67 ERA in six starts. In his previous start, the right-hander allowed two runs and five hits with seven strikeouts in 7 1-3 innings.
It is not yet known when Tomlin began experiencing soreness in the wrist.