In return, the Nationals received minor league right-hander Jacob Condra-Bogan.
Goodwin had appeared in 48 games for the Nationals this season, hitting .200 with three home runs and 12 RBIs.
Condra-Bogan was 1-1 with five saves and a 3.00 ERA in stints with two Class A teams.
The Nationals also announced that they had recalled left-handed pitcher Sammy Solis from Triple-A Syracuse. Solis is 1-1 with a 4.50 ERA for Washington this season.
Goodwin, 27, has a career average of .246 with 16 homers and 47 RBIs in 144 major league games.