The Nationals made the moves before Monday night's game against the New York Mets. Desmond's move was retroactive to Sunday.
Desmond was hitting .286 with 17 home runs, 53 RBIs and 15 steals for the NL East-leading Nationals. He had been trying to play through the injury, but an MRI exam on Sunday revealed a tear.
Danny Espinosa started in Desmond's place against the Mets.
Brown was hitting .300 with 21 homers and 58 RBIs with Syracuse. He was 0 for 3 in three games for Washington this year.