His place, as Wales look for only their fourth Murrayfield victory in 20 years, is set to go to former captain Ryan Jones after he impressed after being introduced for Powell.
But there's better news on Stoddart, one of Gatland's few bright spots from a desperate opening night, as he could yet make the Edinburgh clash despite breaking his hand against England.
Wales physiotherapist Mark Davies said: "Morgan has been given a window of opportunity.
"If his symptoms settle down, we will clear him to play subject to a fitness review later in the week.
"Andy (Powell) needs a period of rest now, but if all goes well he should be back in contention for the Italy game at the end of the month."
If Stoddart does not recover then Cardiff Blues' Chris Czekaj, called into the Welsh squad as cover, could come into the equation or alternatively James Hook or Jamie Roberts could be shifted to the wing.
The battle for the No.8 role seems to be a straight shootout between Jones and Jonathan Thomas but Wasps star Powell warned them not to get too comfortable in his shirt as he targets a quick return.
He said: "Hopefully it's not as bad as everybody first made it out to be, so it will be three weeks probably.
"I'm a good healer so hopefully I will get back for the next game."