The 49ers also re-signed veteran wide receiver Jordan Matthews on Thursday to a one-year contract. Matthews was at practice on Thursday.
Hurd, a rookie, has been dealing with a back injury since training camp. In a preseason game against the Dallas Cowboys, the third-round pick out of Baylor caught three passes for 31 yards and two touchdowns.
Last month, Shanahan had said he was hoping Hurd would be back after the Week 4 bye.
The team did not disclose Verrett's injury, but The Athletic reports that the veteran injured his knee during a Week 3 victory over the Pittsburgh Steelers.
Matthews, who has 270 receptions for 3,255 yards and 22 touchdowns in five NFL seasons, was with the 49ers in training camp but was released before the season.
The 49ers also announced that they had re-signed offensive lineman Will Holden to the practice squad.