Mathis, who currently is serving a suspension for violating the NFL's policy on performance-enhancing drugs, suffered the injury last week while working out, the source confirmed to Schefter.
Indianapolis coach Chuck Pagano acknowledged Monday that Mathis has an Achilles injury but would not confirm that the ligament is torn or that the linebacker is out for the season.
"Really a devastating blow for Robert, his family and our team and this organization," Pagano said. "We hate to lose anybody. This one stings, but like always, nobody is better equipped to handle circumstances and adversity than this group."
Pagano said that the Colts will wait until their doctors meet with Mathis on Tuesday before determining the severity of the injury or announcing how long he will be sidelined.
Mathis' season-ending injury was reported earlier Monday by Pro Football Talk.
The 33-year-old Mathis led the NFL with 19.5 sacks last season, his 11th with the Colts.
But Mathis received a four-game suspension in May, when the NFL ruled that he had violated the league's PED policy by testing positive for Clomid, a fertility drug.
Despite Mathis' appeal through the NFL Players Association, the league upheld the ban, stating that the Pro Bowl linebacker failed to consult with NFL or team doctors before taking the drug.
With Mathis out for the forseeable future, the Colts will turn to second-year player Bjoern Werner.