Washington will send San Francisco a fifth-round pick in return, reports NFL.com's Ian Rapoport.
The Redskins were in need of a tight end after season-ending injuries to both Niles Paul and Logan Paulsen. The only tight end left on the Redskins roster before the trade was Jordan Reed, who has dealt with numerous injuries in his career.
Carrier, who entered the league as an undrafted free agent in 2012, spent two seasons with the 49ers. In his career, he has nine receptions for 105 yards in 16 games. Carrier started one game for San Francisco in 2014.