Groome was optioned to Triple-A El Paso by the Padres on Monday.
Groome was traded from Boston to San Diego in exchange for Eric Hosmer, Max Ferguson and Corey Rosier, Sean McAdam of BostonSportsJournal.com reports.
Groome allowed five hits and three walks while striking out five over six scoreless innings for Triple-A Worcester on Friday.
The Red Sox promoted Groome from Double-A Portland to Triple-A Worcester on Thursday.
Groome allowed one hit and struck out four over five scoreless innings for Double-A Portland on Wednesday.
The Red Sox transferred Groome from Triple-A Worcester to Double-A Portland on Monday.
Groome was optioned to Triple-A Worcester on Wednesday, Pete Abraham of The Boston Globe reports.
Groome was promoted to Double-A Portland and earned the win in his debut Saturday against New Hampshire. He struck out a career-high 10 batters and allowed two hits over five innings.
Groome was beaten up for eight runs (seven earned) in five innings for High-A Greenville against Hickory on Tuesday.