The Diamondbacks outrighted Grace to their alternate training site Sunday.
Grace was designated for assignment by the Diamondbacks on Thursday.
Grace (0-1) took the loss in Saturday's 5-1 loss to the Giants. He failed to retire a batter, giving up three runs on one hit and two walks.
Grace had his contract selected by the Diamondbacks and was added to the major-league roster Wednesday.
Grace was assigned to the Diamondbacks' alternate camp Saturday, Steve Gilbert of MLB.com reports.
Grace will be a part of the Diamondbacks' 60-man summer camp.
Grace signed with Arizona as a non-roster invitee Tuesday.
Grace was outrighted to Triple-A Fresno on Monday, Andersen Pickard of MLBDailyDish.com reports.
Grace was designated for assignment by the Nationals on Friday.
Grace will serve as the Nationals' first-ever opener Saturday against the Dodgers, Jamal Collier of MLB.com reports.