The teenage defender, who was rewarded with his first professional contract in the summer, damaged two parts of the medial ligament in his right knee during Cherries' 4-3 victory.
Although he is unlikely to require surgery, Stephenson is next week expected to see a specialist for a full diagnoses and could be out for between eight to 12 weeks.
Stephenson had only recently hit the comeback trail after recovering from double hernia surgery at the start of last month.
The highly-rated 18-year-old also spent the first five months of last season on the injury list after being crocked in a youth team fixture in August.
Cherries boss Eddie Howe said: It is a big blow for Tim because he has really struggled to keep himself fit and has missed a lot of football.
I feel for him at the moment because he has had a run of bad luck. It would be good to see him get a break and stay fit for a period of time.