To fill his spot on the 53-man roster, the club signed safety Dewey McDonald.
The Patriots are thin at wide receiver, with Julian Edelman expected to miss significant time with a left foot injury, Danny Amendola currently limited after injuring his knee Monday, and fourth-year veteran Keshawn Martin having missed the last five games with a hamstring injury.
As for Dobson, the 2013 second-round draft choice finished the season with 13 catches for 141 yards. He played in eight games, with three starts, appearing in 29.7 percent of the offensive snaps as a No. 3, 4 or 5 option on the depth chart.
Dobson enters the final year of his contract in 2016.
McDonald, 25, was claimed by the Patriots on waivers Oct. 28 and played in two games. His contributions came exclusively on special teams. He was released Nov. 12, returned to the practice squad two days later, then was released from the practice squad when the team needed to import two cornerbacks to account for injuries on the 53-man roster.