He has been ruled out of the ongoing T20 tri-series in Christchurch also involving Pakistan and Bangladesh.
A seam bowling, middle order batsman, Mitchell sustained the blow while batting in the nets and his hand would remain in cast for at least two weeks, New Zealand Cricket said in a statement.
"It's a real shame for Daryl to suffer this injury on the eve of an exciting period of cricket for the side," coach Gary Stead said.
"Daryl's become a really important player to our T20 unit and we're certainly going to miss his all-round skills and versatility in the tri-series.
"With our first game of the World Cup in just over two weeks we need to take some to consider Daryl's recovery timeline and his potential involvement in the tournament."
New Zealand begin their World Cup campaign against champions Australia on October 22 in a repeat of the last year's final.
