McKenzie sustained the injury early in the second half of the Waikato Chiefs' 33-29 Super Rugby win over Auckland Blues on Saturday.
McKenzie has 23 test caps for New Zealand, who begin their World Cup campaign against South Africa in Yokohama on 21 September.
"He's done an ACL and looks to be out for eight to nine months which is a real shame for him," Hansen said.
"His World Cup opportunity's gone but he's still young enough to make probably the next two. It's just important he gets his knee right and takes the time to be able to come back and achieve the dreams that he wants to achieve.
"It's sad for him obviously. It creates another opportunity for someone else. We've got to expect injuries and there will be more than just him I'd say."
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