A fourth-year player out of Minnesota, Wyrick figures to get some action on special teams, but he probably won't play much on defense barring injuries.
The Dolphins chose Wyrick over a couple of other cornerbacks they worked out on Monday, Alex Molden and Jacoby Shepherd.
The Dolphins decided against moving up Alphonso Roundtree from the practice squad for a second time this season.
Roundtree was on the active roster for a couple of weeks but lost his roster spot when the Dolphins re-signed Oronde Gadsden.
Fletcher's season ended when he sustained a broken left forearm in the Thanksgiving Day victory at Dallas.
Also this week, the Dolphins announced that wide receiver J.R. Tolver had undergone surgery on his right patellar tendon.
The rookie from San Diego State was placed on injured reserve several days ago.