Minor league outfielder Eury Perez was recalled from Syracuse and placed on the 60-day disabled list with a left toe fracture. Dobbs will take his spot on the 40-man roster.
Dobbs was signed to a minor league deal four days ago. The 35-year-old is a career .262 hitter spanning 11 seasons with the Marlins, Phillies and Mariners.
He went just 1-for-13 for the Marlins this season before being designated for assignment on April 29.
Dobbs has experience at both the corner infield and corner outfield spots. He leads all active players in pinch-hits with 96 and is a career .247 pinch-hitter.
Leon hit .182 with a homer and three RBIs in 13 games for the Nats. After Wilson Ramos' return from the disabled list, Leon was serving as the Nats' third catcher, and hadn't played since May 5.