Stoddart broke his left leg during Wales’ clash with England at Twickenham on Saturday and was immediately taken to Charing Cross hospital where he was operated on yesterday.
Elsewhere, a trio of former British & Irish Lions have given head coach Warren Gatland a fitness boost ahead of the return clash with England at the Millennium Stadium on Saturday (kick-off 2.30pm).
James Hook (shoulder), Lee Byrne (knee) and Adam Jones (toe) are all back in full training and have been declared fully fit and back in contention for selection, which occurs on Thursday.
Longer term injury victims Leigh Halfpenny (ankle) and Richard Hibbard (shoulder) have also provided good news to the Welsh camp and are targeting returns against Argentina in 12 days time.
“Both Leigh and Richard have come through contact screening and will be fully integrated back into training this week, with a view to being back in contention for the Pumas match,” said WRU national performance medical manager Prav Mathema.
“Both Adam and Lee where back in full training towards the end of last week and James is also now ready to take a full part.”
However, Wales are still waiting on the fitness of Scarlets pair Stephen Jones and Matthew Rees and will re-assess Blues prop Gethin Jenkins later this week.
“Stephen pulled out of the game at the weekend as a precaution with a tight calf, but we need to have a closer look at him in the early part of this week before we make a further judgement,” added Mathema.
“Matthew is making normal progress after his injection (neck), but it is also too soon to make a judgement on him and Gethin is also set to be re-assessed.
“The good news about Morgan is that he has come through surgery successfully and he will now begin his rehabilitation programme back at the Scarlets.
“He travels back from London tomorrow, but it is impossible at this stage to put a time frame on his recovery.”
