The Ospreys back came on after 54 minutes but did not complete the match after being taken off on a stretcher with three minutes remaining following an innocuous-looking tackle.
Walker went for medical assessments on the injury and a medial ligament problem was diagnosed, ruling him out of the tournament in New Zealand which begins next month.
Scotland head coach Andy Robinson, who is to name his 30-man World Cup squad on Monday, said: "Nikki has worked exceptionally hard in training and some of the running lines he made yesterday when he came off the bench were first-class.
"It's obviously disappointing for Nikki.
"We all feel for him but injuries do happen in sport and you just have to deal with them. We wish Nikki a speedy recovery."
Walker won his 24th cap on Saturday and has scored six Test tries, including in March's win over Italy in the RBS 6 Nations.
The 29-year-old will now return to his club, where he will undergo further assessments and the Ospreys medical team will lead his rehabilitation.
The injury means Robinson now has seven players to cut from his preliminary squad for the World Cup.
Scotland's Pool B campaign begins against Romania on September 10 in Invercargill.
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