In exchange, the Commanders are receiving a 2026 sixth-round pick.
Robinson rushed for a career-high 799 yards and eight touchdowns as the starting running back for the Commanders last season.
The 26-year-old is entering his fourth season after Washington selected him in the third round of the 2022 NFL Draft.
Washington will look towards veteran Austin Ekeler and rookie Jacory Croskey-Merritt to carry the workload this year, with veteran Jeremy McNichols to receive carries as well.
The Commanders had the third-best run game in the NFL last season, posting 154.1 rushing yards per game and 2,619 yards on the ground in total, with the fourth-most touchdowns (25).
Meanwhile, San Fran is trading for whoever they can as their offence is currently decimated with injuries.
Earlier this week, the team traded for wide receiver Skyy Moore following Demarcus Robinson's suspension, and is dealing with four injuries to other receivers, including their main man in Brandon Aiyuk, who is "eyeing a Week 6 return."