The 25-year-old scrum-half will act as back up for Edinburgh team-mate Mike Blair, who is set to skipper Scotland against the number one ranked side in the world on Saturday.
Laidlaw has featured in seven of his club's Magners League matches so far this term, starting the home wins over Aironi, Ulster and Treviso.
The former Scotland Sevens star becomes the second uncapped player in the 22 alongside Glasgow stand-off Ruaridh Jackson.
"You feel for your team-mate in a situation like this, but it's clearly a great chance for me and one I'm determined to take if I get game time," said Laidlaw, a nephew of ex-Scotland and Lions No9 Roy Laidlaw.
"This is obviously disappointing for Rory but there's now an opportunity for Greig, who is tenacious and fiercely competitive and has shown the skills and mindset on his appearances for Scotland A and Scotland Sevens and on his performances for Edinburgh to underline his credentials," added Scotland head coach Andy Robinson.
Scotland face the All Blacks, Springboks and Samoans at Murrayfield this month as they look to build on a famous win over Ireland at Croke Park and an historic series triumph in Argentina.
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