It is expected he will miss Glasgow's two Heineken Cup matches next month - against Northampton Saints at Hughenden on October 24 and the away game against Toulouse five days later.
Glasgow coach Hugh Campbell said: "It is an enormous setback for the squad and a personal tragedy for Paul. He had put in his best performance for us. Apart from scoring our first try, his general play was outstanding."
Scottish newspaper The Daily Record reports that Campbell is considering signing South African Johan van der Schyff as cover fro Dearlove.
Van der Schyff, primarily a blindside flanker, has played for South Africa at school and under-19 levels.
Campall is reported to have watched Van der Schyff made his debut for Currie against Hawks at the weekend, less than a week after the South African arrived in Scotland. Van der Shyff could now be in line for a place in Glasgow's squad for the initial stages of the Heineken Cup, which kicks off in less than three weeks. The deadline for European Cup registration arrives at the end of this week.