Miami received right-handed minor league closer Kyle Barraclough from the Cardinals as part of the deal.
Cishek, 29, went 2-6 with three saves and a 4.50 ERA in 32 appearances for Miami this season.
The right-handed, sidearm slinger has a career record of 17-20 with 94 saves and a 2.86 ERA in 284 appearances.
To make room for Cishek on the team’s 40-man roster, the Cardinals have transferred pitcher Matt Belisle to the 60-day disabled list. Once Cishek joins the Cardinals active 25-man active roster, the team will announce a corresponding roster move.
Barraclough, 25, has split time between Single-A Palm Beach and Double-A Springfield this season, combining for a 3-0 record with 12 saves and a 2.27 ERA.
The Santa Clara, CA, native was a seventh-round selection of the Cardinals in the 2012 First-Year Player Draft. In 100 career minor league games, he has amassed a 5-6 record with 25 saves and 2.82 ERA.