The Brewers optioned Hudson to Triple-A Nashville on Wednesday.
Hudson was sent out to the minors to make room on the active roster for right-hander Logan Henderson, who was recalled from Nashville to make a spot start Wednesday against the Guardians. The lefty reliever was with the Brewers for less than a week after being promoted last Friday, making his lone appearance in Monday's 5-0 loss to Cleveland. He struck out four and allowed one earned run on one hit and three walks over 1.2 innings.