The 31-year-old came on as a second-half substitute in the 13-12 defeat by Toulouse on Saturday but was forced off the field 15 minutes later after sustaining the injury.
It means the Pumas star will miss next month's Test matches against England, Wales and Italy.
A statement on Toulon's official website said: "Hit against Toulouse on Saturday, flanker Juan Martin Fernandez Lobbe has suffered a fracture of the right elbow.
"He will see a doctor in a Marseille to have an operation. His unavailability is estimated at two to three months."