The Royals also sent catcher Adam Moore to the Padres on Tuesday for cash considerations.
Schuster, who has not pitched above Class A, was placed on the 40-man major league roster. To clear roster space for Schuster, the Royals designated for assignment outfielder Carlos Peguero.
The 23-year-old Schuster had a 1.83 ERA in 55 games last year for Visalia in the California League. He struck out 45, allowed 30 hits, and walked 18 in 44 1-3 innings.