This award recognizes the most outstanding relief pitcher during each month of the regular season as voted on by a panel from Major League Baseball.
Soriano did not allow a run in his 12 appearances during May, converting each of his nine save opportunities to tie for the American League lead in saves for the month.
Tuesday night, Soriano picked up his 15th save in 15 opportunites this season.
"To me, right now, I feel real comfortable," Soriano said.
When asked to describe what he has seen of Soriano this season, manager Joe Maddon said: "Very composed. Very calculated. Knows exactly what he wants to do. ... He's definitely a one-pitch-at-a-time guy."