Johnson suffered a fracture in the European Champions Cup defeat to Montpellier which saw the Warriors go down 36-26.
It is not a good prognosis for the 24-year-old Australian, who was playing in what was essentially a dead rubber contest, as the Scottish side are already out of the competition.
Boss Dave Rennie had described Johnson as "probably our best midfielder in the first three months" of their PRO14 campaign, so it will be a huge blow to the remainder of their season.
The injury list continues to mount for the Warriors with Stuart Hogg, Callum Gibbins and Leonardo Sarto among a dozen injury absentees.
Johnson is expected to return to action in late February, meaning he will miss the rest of the Champions' Cup campaign.