Stoddart sustained the injury playing against Edinburgh in the Magners League in early March at Parc y Scarlets.
The talented Welsh international full-back had hoped to be back earlier than first expected in the autumn, however an infection in the site of the injury has meant that his comeback has been delayed while he undergoes treatment.
Patrick Moran, the Scarlets physio said: "The knee operation went well and the good news is that despite this really nasty injury, Morgan's knee ligaments have been repaired successfully and the knee is stable.
"Unfortunately, there has been an ongoing infection in part of the injury site and so this has delayed his rehab over the summer. It's being treated with antibiotics and is looking better."