Marshall hasn't played since Sept. 30 because of a back injury. Marshall has a blood clot in his back, according to the Sentinel's Omar Kelly.
"Stressful. That's the only word you can use to describe it," Marshall told the Sun Sentinel. "I can't practice, even if I wanted to. I can do certain things, but I can't do everything that I need to do to be out there."
In four games this season, Marshall, who is in his first season with the Dolphins, had 17 tackles and one interception. The seven-year veteran spent five years with the Carolina Panthers and one year -- 2011 -- with the Arizona Cardinals.
Before this season, Marshall had never missed an NFL game.
To replace Marshall, the Dolphins claimed cornerback Brandon McDonald off waivers Wednesday. He was released by the Tampa Bay Buccaneers on Tuesday.