Suh, a three-time All-Pro, tweeted Monday morning in a video: "There will be some exciting things going on."
Suh, 31, signed a six-year, $114.4 million contract in 2015 but totaled only 15.5 sacks in the last three seasons. He made the Pro Bowl in 2016.
The timing of the move is puzzling because the Dolphins will save only $3.9 million in salary cap space with a $22.2 million penalty. If they waited until June 1 to release Suh, $9.1 of the $22.2 million of dead money would count against the 2018 cap with the remaining $13.1 million against the 2019 cap.
This will be the third significant move Miami has made toward changing the culture of the locker room.
The Dolphins traded running back Jay Ajayi to the Super Bowl champion Philadelphia Eagles for a fourth-round pick Oct. 31 and sent wide receiver Jarvis Landry to the Cleveland Browns for two draft picks in a transaction that will become official Wednesday when the league opens its 2018 season for business.