The 19-year old, who enjoyed a breakthrough season in 2015-16 with 13 appearances and two tries, has ruptured his anterior cruciate ligament.
Watkin signed his first professional contract with Ospreys in April, having helped Wales Under-20s win the 2016 Six Nations Grand Slam.
He will undergo surgery in the next couple of weeks.
Ospreys centre Owen Watkin faces a long lay-off after sustaining a serious knee injury in training.