Jones sustained the injury during Sunday's 24-17 setback to the Chicago Bears at Soldier Field. The loss eliminated the Packers (5-8-1) from postseason consideration.
Per the Milwaukee Journal Sentinel, Jones' leg was straight at the moment of impact on a tackle.
Jones, who exited after rushing for eight yards on four carries, said the injury felt similar to the one he sustained to his MCL during the 2017 season.
The 5-foot-9, 208-pound Jones has rushed for 728 yards and eight touchdowns this season while adding 26 receptions for 206 yards and a score.
Jamaal Williams rushed for 55 yards and a touchdown on 12 carries against the Bears while adding four receptions for 42 yards.
The 23-year-old Williams has rushed for 365 yards and two touchdowns this season while adding 18 receptions for 133 yards.
The Packers have fullback Danny Vitale on the roster and running backs Lavon Coleman and Malcolm Johnson on the practice squad.
Green Bay signed receiver Allen Lazard from the Jacksonville Jaguars' practice squad to take Jones' roster spot. Lazard signed with Jacksonville as an undrafted free agent out of Iowa State in the spring.