The No. 8 was stretchered from the field during the RBS Six Nations match against Ireland last weekend.
Initial medical reports suggested ligament damage, and a lengthy break.
Taylor underwent surgery 24 hours after the incident. The surgery involved the repair of the ruptured anterior cruciate ligament.
Scotland team doctor, James Robson, said: 'This is the type of injury, similar to Andrew Mower's ahead of the Rugby World Cup, that has happened to a number of players including Nathan Hines and Marcus Di Rollo.
'We are pleased that Simon underwent surgery so quickly after the injury took place and we are feeling very positive about the prognosis. Simon is now looking ahead to the hard work that faces him with SRU physios Stuart Barton and Stevie Mutch on his recovery to full fitness.'
The normal course of recovery for an injury of this type is in the region of eight to nine months.
'Simon's injury is severe,' said Scotland coach Matt Williams after their 37-16 defeat. 'He's in a lot of pain.'
The news is a major blow to the Gunners hopes of beating the European champions.
Taylor is likely to be replaced in the Gunners line-up by Allistair Hogg, who has impressed in the Celtic League this year.