Russell sustained the injury playing for his French club Racing 92 on Sunday and has not cleared the concussion protocols.
"The 26-year-old playmaker has not satisfied the requirements of today's component of the graduated return to play protocol... meaning there is insufficient time for him to be considered for this weekend's action," Scottish Rugby said in a statement on its website.
Women's Six Nations Championship
Lillicrap: Better times ahead after heavy France defeat
04/04/2021 AT 11:45
Women's Six Nations Championship
England's Itoje to miss final Six Nations clash with Scotland
11/03/2019 AT 10:24
Women's Six Nations Championship
England prepare for life without Mako Vunipola ahead of Wales clash
13/02/2019 AT 11:03