Hasty suffered a broken collarbone during the fourth quarter of Sunday's 27-13 loss to the New Orleans Saints. Head coach Kyle Shanahan said Hasty will have surgery and is done for the season.
Cyprien suffered a hamstring injury.
San Francisco signed Hasty as an undrafted free agent out of Baylor in April. He started the season on the practice squad but was promoted to the active roster on September 26.
Hasty finished the season with 39 carries for 148 yards with a rushing touchdown while adding seven receptions for 33 yards through six games. He has been active in eight games but did not touch the football during Weeks 4 and 5.
The 49ers remain hopeful that running backs Raheem Mostert (ankle) and Tevin Coleman (knee) will return after the bye week.
San Francisco signed Cyprien on August 20. The veteran appeared in four games this season, recording two tackles and a forced fumble.
The 49ers also placed safety Jared Mayden on the practice squad injured list, which is similar to injured reserve. He suffered a quad injury during Sunday's game after being activated from the practice squad. Shanahan said Mayden is expected to miss a few weeks and might have a chance to return this season.
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