Suter signed a one-year, $2.25 million contract with the Reds on Friday.

The Reds reinstated Suter (shoulder) from the 15-day injured list Sunday.

Suter (shoulder) has been sent to Triple-A Louisville to begin a rehab assignment.

Suter (shoulder) had a good bullpen session Monday in Toronto and could begin his rehab assignment by the end of the week, Gordon Wittenmyer of The Cincinnati Enquirer reports. "The international pen was solid. Not unbelievable, but solid," Suter said. "Felt real good."

Suter (shoulder) will need at least three rehab outings before being activated off the 15-day injured list, C. Trent Rosecrans of The Athletic reports.

Suter (shoulder) will throw a live batting practice session Friday, Charlie Goldsmith of the Cincinnati Enquirer reports.

Suter (shoulder) has begun throwing, MLB.com reports.

The Reds placed Suter on the 15-day injured list Saturday with a partial tear of his left teres major muscle.

Suter will serve as the Reds' opening pitcher for Thursday's game against the Dodgers, Gordon Wittenmyer of The Cincinnati Enquirer reports.

Suter allowed four hits and one walk while striking out two over 3.1 relief innings in Sunday's 3-0 win over the Angels.