The Dolphins also released linebacker Lawrence Timmons after just one season with the team, multiple media outlets reported, although his release is not as surprising as the release of Suh.
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.
The release of Timmons was expected. He was suspended for a game in 2017 after he went AWOL a day before the team's opener against the Los Angeles Chargers.
Timmons, 31, signed a two-year, $12 million contract with the Dolphins last season after leaving the Pittsburgh Steelers. His release saves $5.4 million in salary cap room.
A Pro Bowl selection in 2014, Timmons played in 14 games for the Dolphins, all as a starter, and had 84 tackles. He has 35.5 career sacks, but he did not record a sack in 2017.
The release of Suh and Timmons continues the Dolphins' attempt to change 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.