A scan revealed a ruptured anterior cruciate ligament and a torn meniscus.
She has been replaced by Sarah Burke for the remaining games in Australia, but Auckland's Ros Kember will deputise in England next month.
The White Ferns have a busy schedule ahead with four matches to go in the Rose Bowl, then three Twenty20 internationals and six 50-over games in England in the space of 18 days.
The loss of Milliken is a major blow to their chances as she is the quickest bowler in the team, with 60 wickets to her credit in one-dayers and Twenty20 matches.
And the news that she faces a long spell out of the game compounded the disappointment of a comprehensive seven-wicket defeat in the opening game against Australia.
They managed only 132 all out after winning the toss in Darwin and Australian knocked off the runs with 17 overs to spare as Lisa Sthalekar made an unbeaten 45.