He has previously played in Nippon Professional Baseball (NPB) for the Fukuoka SoftBank Hawks and Hanshin Tigers.

[citation needed] On November 2, 2015, Suarez signed with the Fukuoka SoftBank Hawks of Nippon Professional Baseball (NPB) .

[citation needed] Suarez finished the 2019 regular season with 9 Games pitched, a 0–4 Win–loss record, a 5.74ERA, and 27 strikeouts in 26 2/3 innings.

[13] On June 30, Suárez’s streak ended when he came in to pitch in a tie game, with the new record being set at 14 consecutive mound appearances with a save.

[16] On July 12, Suárez was placed on the 60-day injured list after undergoing knee surgery to remove "loose impediments" the month prior.

[20] After suffering from arm stiffness and right elbow inflammation during spring training, Suárez began the 2023 season on the injured list.

[23] On August 23, Suárez was ejected for a sticky substance following a glove check, and received a 10–day suspension, which he unsuccessfully appealed.