Wilson was forced off at halftime in the 22-13 loss on Saturday as Scotland suffered a major setback to their title aspirations.
Centre Huw Jones and fullback Stuart Hogg suffered knee and shoulder ligament injuries respectively in the same game, the SRU added, but both remain part of the squad and will be assessed by a specialist this week.
Scotland next play against France in Paris on Saturday, Feb. 23 and then have Wales at home and England away.
(Reporting by Mark Gleeson; Editing by Christian Radnedge)
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