Mitchell will be the only player named in the T20 World Cup squad who will be playing in a second-string ODI side for the three-match series.
Black Caps stand-in coach Glenn Pocknall said the injury comes as a blow ahead of the ODI series.
"Everyone is gutted for Tom, he's a quality player with a diverse skill set. He'll remain with the squad and we're hopeful he'll be available again for the T20 series."
Pocknall said after consultation with regular Black Caps coach Gary Stead it was agreed Mitchell was best suited as a replacement.
"He has shown last summer what a destructive batsman he is, while also offering another useful bowling option. With Tom out, we do lose our first choice back-up wicketkeeping option.
"However there are several guys in the squad with keeping experience and we'll ensure they do the necessary work at training to be up to speed if called on."
The Black Caps start their ODI series against Pakistan at 9.30pm tomorrow night.