Gurley is dealing with a thigh contusion that he suffered in a Week 5 loss to the Seattle Seahawks.
Brown has rushed for 114 yards and two touchdowns on 26 carries. Henderson has played only two snaps this season, both in a Week 1 win over the Carolina Panthers.
On Saturday, the Rams also made a roster move to add depth at running back, promoting John Kelly from the practice squad to the active roster. In a corresponding move, receiver Nsimba Webster was waived.
Gurley's absence leaves the Rams without several key starters against the undefeated 49ers. Cornerback Aqib Talib has been ruled out because of a rib injury and outside linebacker Clay Matthews also is sidelined after undergoing surgery to repair a broken jaw.