Givens' injury occurred in the first quarter. Also suffering a high-ankle sprain was running back JaMycal Hasty. Shanahan doesn't expect either to return soon.
"Kevin Givens had a high-ankle [sprain]," Shanahan said. "He'll be out for a while. Same thing with JaMycal Hasty—high-ankle."
Shanahan also provided injury updates to several 49ers running backs, a position group seemingly hit hard on Sunday. Elijah Mitchell, Trey Sermon, and Hasty each left the game. However, Mitchell did return following the injuries to the other two.
Mitchell is "day to day" with a shoulder injury. Sermon is in the concussion protocol.
"Arik Armstead had an abductor," Shanahan added. "We'll be the same this week as we were last week with him. Javon Kinlaw, knee. We'll have to manage him this week. Josh Norman had an ankle. He's day to day. Hoping to get [Emmanuel] Moseley back this week."
Emmanuel Moseley has been inactive the first two weeks due to a knee injury.
49ers hosting three RBs for visits
ESPN's Adam Schefter reported today that the 49ers are going to host two free-agent running backs, Duke Johnson and Lamar Miller, for visits.
Johnson has been in the league since 2015 and had stints with the Cleveland Browns and Houston Texans. He was briefly with the Jacksonville Jaguars this month before being released last week.
Miller has been in the league since 2012 and spent time with the Miami Dolphins, Texans, Chicago Bears, and Washington Football Team. Washington released him on August 15.
Shanahan added that the 49ers also worked out former Buffalo Bills running back T.J. Yeldon.