Sherman, who experienced tightness in his hamstring during Friday's practice, will miss the 49ers' preseason opener against the Dallas Cowboys on Thursday night.
The four-time Pro Bowl selection will "progress back" next week, according to the team.
Also on Sunday, the 49ers announced they signed guard Chris Gonzalez to a one-year deal and waived safety Corey Griffin.
Sherman signed a three-year, $39 million contract with the 49ers just two days after he was released by the Seattle Seahawks.
The 30-year-old Sherman helped the Seahawks win a Super Bowl title following the 2013 season and led the club back to the championship game the following year.
Sherman was a fifth-round pick (No. 154 overall) out of Stanford in 2011. He has 32 interceptions and 99 passes defensed in his career.
Gonzalez, who is listed at 6-foot-3 and 310 pounds, originally was signed by the Minnesota Vikings as an undrafted free agent on April 30. He was released on July 28.
The 23-year-old appeared in 44 games over five years at San Jose State. He earned Honorable Mention All-Mountain West honors after starting all 13 games in 2017.