The 26-year-old Edinburgh back-row suffered the injury in the first half of the EMC Test defeat to the world champions.
Asked about Rennie's withdrawal, Robinson said: "He dislocated his shoulder."
Rennie was winning his 20th cap and was hurt in the build-up to New Zealand's first of six tries, which was scored by Israel Dagg.
He was replaced by David Denton, his Edinburgh team-mate, and the length of absence is to be determined.
Scotland's next Test is against South Africa on Saturday, with the final fixture of the year on November 24 against Tonga in Aberdeen.
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