Akers suffered the injury while working out and underwent testing to confirm the diagnosis, the source told Schefter.
The Rams announced Akers' injury Tuesday morning but did not disclose an official timeline for how long he will be out.
Akers was expected to be the focal point of the Rams' running game this season after his breakout rookie campaign, when he averaged 113.1 yards from scrimmage over the final seven games, including the postseason.
Rams coach Sean McVay said later Tuesday, during an interview with 710 ESPN in Los Angeles, that he feels "so bad" for Akers because "he's doing everything right" and "working hard."
McVay also indicated that the Rams initially would look in-house to replace Akers. Los Angeles' running backs entering training camp next week will be Darrell Henderson Jr., 2020 undrafted free agent Xavier Jones, rookie Jake Funk, Raymond Calais and undrafted rookie Otis Anderson.
McVay said he was "intrigued" by the younger running backs, although he did not rule out Los Angeles eventually considering a veteran addition. Among the veteran running backs currently available as free agents are Adrian Peterson, Le'Veon Bell, LeSean McCoy, Devonta Freeman and former Rams star Todd Gurley.
"We've got some young backs on our roster that I'm intrigued about seeing how they handle this opportunity," McVay told 710 ESPN. "I don't know that the veteran route is something that we'd rule out, but it's not something we're immediately looking to address right now."
In 13 regular-season games total, Akers was the Rams' leading rusher with 625 yards and two touchdowns on 145 carries. He also caught 11 passes for 123 yards and a touchdown.
The 5-foot-10, 217-pound Akers also had 272 yards from scrimmage and scored two touchdowns in the Rams' two postseason games.
Akers, 22, spent two games sidelined after suffering a rib injury in Week 2 when he awkwardly fell on the football. He also played through a high ankle sprain later in the season.
Selected in the second round (No. 52 overall) of the 2020 draft from Florida State, Akers shared time last season with Henderson and Malcolm Brown.