Clinton-Dix, 25, has been a starter since his rookie season in 2014, and he becomes an unrestricted free agent after this season. He was a first-round draft pick and made the Pro Bowl in 2016.
The Redskins are in first place in the NFC East with a 5-2 record.
During his Pro Bowl season, Clinton-Dix had five interceptions, but he had a down year in 2017 as the Packers' entire defense struggled. He's off to a better start this season with three interceptions, a sack and a forced fumble in the first seven games.
Clinton-Dix has been reliable, playing all but eight defensive snaps last season. He once had a streak of 2,033 consecutive defensive plays on the field.
The Redskins have D.J. Swearinger, who has played at a high level most of the season as an in-the-box safety who occasionally must play deep. He has intercepted four passes, including two in Sunday's win over the New York Giants. Second-year player Montae Nicholson has started every game at free safety and gives Washington speed in the middle, but he hasn't made the impact the team had anticipated this season in terms of big plays. Multiple sources say Nicholson has been "banged up" this season. Nicholson missed nine games last season due to a shoulder injury and a concussion, the latter of which caused him to be placed on injured reserve in December.
Clinton-Dix gives the Redskins another player who can perform both safety roles.
The real issue has been depth. Washington placed rookie Troy Apke on injured reserve Monday with a hamstring injury. The Redskins have Deshazor Everett as their main backup. He's considered a special-teams standout. Until this trade, their fourth safety was undrafted free agent Kenny Ladler, another special-teams performer.
Even after this trade, Washington should have 10 draft picks next offseason; the Redskins hope to land four compensatory picks based on last offseason. They've placed a greater emphasis on acquiring compensatory picks. If Clinton-Dix leaves in free agency and signs a big contract elsewhere, the Redskins could be in line for another compensatory pick in the 2020 draft.
The Packers have let their last two high-priced safeties -- Morgan Burnett and Micah Hyde -- leave in free agency. Clinton-Dix likely will want a deal next season that comes in at around $8 million per year.
The move leaves the Packers with former undrafted free agents Kentrell Brice and Jermaine Whitehead as their top two safeties. It could mean more playing time for 2017 second-round pick Josh Jones, who has played primarily on special teams this season.
The Packers also traded running back Ty Montgomery to the Ravens on Tuesday.
ESPN's Rob Demovsky and John Keim contributed to this report.