Bond said New Zealand coach Mike Hesson had been "ultra-supportive of the move" because he understood the impact being away from home could have. "When you're away 200-250 days a year, it's certainly demanding. That's not to say I don't love the role but now I've got a gig where I can still do the job I love and get that time at home.
"I'm still hoping to have some role helping bowlers out in New Zealand."
Mumbai will be coached by former Australian captain Ricky Ponting this season, which is expected to start in April. Bond is the bowling coach and former South African player Jonty Rhodes is the fielding coach.
Bond played one season of IPL cricket in 2010 with the Kolkata Knight Riders.
His departure comes as a blow, given the success the New Zealand pace attack has enjoyed under his tutelage.
NZC's head of cricket Lindsay Crocker said his organisation had been anxious to retain Bond's services.
"Make no bones about this - we're very disappointed to be losing Shane," he said.
Bond joins Allan Donald and Damien Wright in exiting the New Zealand bowling coach role since the 2011 World Cup.