Wise, 26, posted a 9.00 ERA over seven innings in six Grapefruit League games. The Australia native struck one, walked one and allowed two home runs.
Wise, who is not on the Major League roster, signed a Minor League contract with the Twins in November.
He spent the previous seven seasons in the Tigers' organization, and has a career 3.37 ERA with 227 strikeouts in 424 1/3 innings in the Minors. In 61 2/3 innings in Triple-A last season, Wise had a 1.90 ERA with 39 strikeouts, 28 walks and three homers allowed.
The Twins now have 38 players in camp: 17 pitchers (two non-roster), five catchers (two non-roster), 10 infielders (four non-roster) and six outfielders (one non-roster).