The injury was sustained in Edinburgh's 22-16 win over Connacht at the Galway Sportsground last Friday. Taylor will begin rehabilitation with the Gunners' medical staff.
Scotland coach Frank Hadden said: "Clearly it's a blow to lose Simon from our tour to South Africa. It's tough news for him as he has worked so hard to regain his fitness and form after the injury which caused his premature departure from last year's Lions tour. During the Six Nations Championship he was beginning to look like his old self again. I wish him a speedy recovery."
Taylor, 26, who won his 46th cap in Scotland's victory over Italy in March, said: "It sounds like I'll be spending a bit of time taking it easy before immersing myself in the rehabilitation programme. It (the injury) is just part of life. It's not the end of the world."