Nugent tore his ACL and sprained his MCL in his right knee, the source said.
Nugent was carried off the field by his teammates Sunday after hurting his knee on an onside kick in the fourth quarter of Cincinnati's loss at Indianapolis.
Coach Marvin Lewis did not have details about the injury Sunday but said it did not look good.
For the season, the 28-year-old Nugent was 14-of-18 on field goals, including a perfect 11-for-11 on kicks of 39 yards and under. He also made all 15 extra points he attempted.