Finnegan started 12 games for Miami last season and recorded 44 tackles with zero interceptions.
He signed a two-year, $11 million contract with Miami last year, but he finished only one season of his contract. The release will save the Dolphins more than $5 million in cap room. Finnegan was due $5.475 million in salary this upcoming season.
This move also marks the third veteran with a significant salary cut by the Dolphins in the past few days.
Last week, the Dolphins also released starting wide receiver Brian Hartline and slot receiver Brandon Gibson in an effort to create cap room before the start of free agency on March 10.
The Dolphins also released backup guard Nate Garner on Monday. The move saves the team about $1.65 million in salary-cap space.