Stoddart's absence limits the options available to Gatland but presents an opportunity to Cardiff Blues' Alex Cuthbert and potentially Scarlets teammate Liam Williams.
Scarlets head coach Nigel Davies revealed he didn't think Stoddart would make his comeback for his club until after the Six Nations is well underway.
He said: "Morgan won't be available until about late February or March.
"He hasn't had a setback and in fact he has had some good news. He had a scan recently and the calcification of his bones is very good.
"He has started running, very gingerly at the moment which will help his recovery but it won't be until February or March when we will see him back."
There is better news for Gatland about winger George North, who will return for Scarlets' Heineken Cup match against Munster on Sunday.
The 19-year-old winger suffered a dead leg in Wales' 18-24 defeat to Australia in a friendly earlier this month.
He missed Scarlets' 17-14 defeat to Munster in Llanelli last Saturday but faces a late fitness test ahead of the clash at Thomond Park.
Davies said: "There is a very strong likelihood George will be available. We tested him on the morning of the game last weekend, but he didn't quite come through.
"We are hoping it is different this week."