The 29-year-old sustained the injury just10 minutes into the Stormers' Super 14 clash with the Chiefs on Saturday.
Jantjes, who could also have appeared for Western Province against the Lions on June 13, was involved in a collision with Liam Messam that will see him spend at least six weeks on the sidelines.
Jantjes currently has 24 international caps to his name and was the heavy favourite to start against the Lions this summer having replaced Percy Montgomery as his country's No1 full back.
Montgomery retired from international rugby last season and Springbok head coach Peter de Villiers will now have to reassess his selection choices ahead of the most-eagerly anticipated Test series.
The injury to Jantes could now mean a Springbok berth for likes of Zane Kirchner of the Bulls, Louis Ludik of the Golden Lions' or the Sharks' 33-year-old former Osprey Stefan Terblanche.