Pena missed a handful of games earlier this season with the same ailment, but did not go on the DL that time.
Pena is 1-1 with a 6.20 ERA in 17 relief appearances, with 17 strikeouts. Trying to maintain a one-run deficit late in Friday's game at Toronto, Pena gave up an insurance run to the Blue Jays.
Harrell has been impressive in nine outings (eight starts) at Charlotte, going 4-2 with a 3.54 ERA. He was 1-0 with the White Sox last season, posting a 4.88 ERA in eight appearances (three starts).
Harrell was initially in the mix for the fifth starter spot this spring but fell out of contention when he struggled in Cactus League play.
On Saturday, manager Ozzie Guillen said that Pena's struggles were preventing him from continuing with the six-man rotation that has done well for most of the past 2 1/2 weeks.
The White Sox have just two effective right-handed relievers in Jesse Crain and Sergio Santos, and with Santos closing games now, Crain is the only one that is available in the seventh and eighth innings to protect leads against right-handed hitters.
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000.