Komatsu was designated for assignment on Sunday to make room for right-hander Jeff Manship on the roster.
As a Rule 5 Draft pick, Komatsu had to be offered back to Washington for $25,000 after he cleared waivers.
Komatsu, 24, was acquired by Minnesota via waivers from St. Louis on May 4 after he was designated for assignment by the Cardinals, who selected him in the Rule 5 Draft from the Nationals in December.
Komatsu hit .219 with one RBI and four walks in 15 games with the Twins. The Nationals assigned Komatsu to Triple-A Syracuse.