General manager Mike Rizzo made the announcement.
Carpenter is 0-0 with a 1.50 ERA in eight games with the Nationals. Acquired from the New York Yankees on June 11, Carpenter is 0-1 with a 4.01 ERA in 30 games this season.
Carpenter and his wife, Brittny, welcomed their first child, Darrell David Carpenter IV, on Monday.
Hill is 0-0 with a 3.75 ERA in six games with Washington this season.
The Nationals open a three-game series against the Orioles on Friday in Baltimore.