The 24-year-old had signed to play for Somerset in the second half of the T20 Blast, but will not now do so, and will miss New Zealand's remaining one-day internationals in England.
Anderson was hurt during the first Test defeat by England at Lord's last month.
The all-rounder had been receiving treatment from the New Zealand medical staff in the UK.
"Obviously this is a blow for both Somerset and Corey but injuries happen in sport," said Somerset director of cricket Matt Maynard.
"We wish Corey a speedy recovery and I can assure all members and supporters that we are actively seeking a suitable replacement."
New Zealand's Corey Anderson is to fly home from their current tour of England for treatment on a back injury.