The injury occurred in the 28th minute of the match when Libbok was tackled high by Toulon's Yannick Youyoutte, who was subsequently sent off for the dangerous tackle.
Libbok was stretchered off the field and taken to a nearby hospital for evaluation. The Stormers later released a statement confirming that Libbok had suffered a concussion and was being monitored overnight.
Losing Libbok is a big blow for the Stormers, who are already without Springbok scrumhalf Herschel Jantjies, who is recovering from a hamstring injury.
The Stormers will be hoping that Libbok's injury is not serious and that he will be able to return to action soon.
It is not clear how long Libbok will be out of action, but the Stormers have a number of other flyhalves in their squad, including Kade Wolhuter and Damian Willemse.