Thursday's moves come a day after Hinckley faced two batters, giving up a hit and a bases-loaded walk, in Washington's 10-3 loss at the Los Angeles Dodgers.
Once considered the Nationals' top pitching prospect, Hinckley had a 4.66 ERA with 11 walks in 9 2/3 innings this season.
The 39-year-old Villone signed with Washington as a minor league free agent last month. He is 56-59 with a 4.75 ERA across 14 seasons with 11 major league clubs.
This is the latest in a series of roster moves made by the majors-worst Nationals in a bid to stabilize a struggling bullpen.