Both players were injured in Saturday's rearranged fixture against Wales.
Racing 92 player Russell suffered a groin injury as he made his first start for the Dark Blues in over a year during Saturday's win over Wales in Llanelli.
Russell was replaced by Hastings, but the Glasgow stand-off did not finish the 14-10 victory in the final game of this year's delayed Six Nations either after suffering a dislocated shoulder.
The Scots kick off their Autumn Nations Cup campaign away to Italy a week on Saturday before also taking on France and Fiji in the one-off eight-team tournament.