Scarlets Medical Officer, Mark Ridgewell has reviewed scans of Stoddart's left hamstring injury and gave teh following assessment:
"Morgan has a grade two hamstring strain. It's a common muscular injury, particularly amongst backs. We have already started treatment, including some anti-inflammatory injections to help us get his rehab process underway in the most effective and expedient way possible.
"This doesn't have any impact on Morgan's former injury, it's the opposite leg."
Stoddart will not require any surgery, just rest and a bespoke rehab programme.
"This is obviously disappointing and frustrating for Morgan, as he was getting back to top form again but thankfully it's only a relatively minor muscular injury," added Scarlets head coach Nigel Davies.
"He will be working closely with our medical team to get back as soon as possible.
"It's too early to say whether he will be fit for our big Heineken Cup fixtures in December and we will know more in a fortnight - but we can be hopeful.
"As frustrating as it is to have some players side-lined, it's rugby and we will pick up injuries. We are in a much better position than we were last season.
"We've got more depth to our side this season, and a number of talented young players within our squad have shown what they are capable of in our last few games. They are pushing for first-team places and will relish the opportunity to step-up.
"As I've said previously, it's important that we all back these players as they gain experience. From what they've shown already, they will play for the Scarlets jersey with spirit and commitment and will be eager to play their part in some crucial and challenging games ahead."