The pair, who struggled in the first Test, will be replaced by Stuart Broad and James Anderson in the two changes to the team that lost by 189 runs in Hamilton.
"It was a very tough call," England captain Michael Vaughan told reporters on Wednesday. "I had a gut feeling we needed a change. I felt that the attack needed a shake-up."
The 29-year-old Harmison has struggled with injuries and loss of form since reaching the top of the world Test rankings in 2004.
He has taken 212 wickets in 57 Tests at an average of 31.39. Hoggard, 31, has claimed 248 Test wickets in 67 matches at 30.50.
The pair however, took just two wickets in the first Test at Seddon Park and conceded 278 runs.
"It was not a nice thing for me to do to go and tell two players I have basically played my entire test career with that they're not in the team," said Vaughan.
"They're just not bowling to the standards they have set themselves."
The 23-year-old Broad, the son of former England opening batsman Chris, has played just one Test match - in Sri Lanka last Dec, while Anderson was released from the squad during the first Test to play a New Zealand first-class match.
"He (Anderson) had overs under his belt in the last week," said Vaughan. "We have seen Jimmy Anderson play international cricket for a while and he has a hell of a lot of talent.
"He deserves his chance and will be looking to establish his presence in the test team for the future."
England's pace bowling attack of Anderson (20), Ryan Sidebottom (11), and Broad (1) have accumulated just 32 Test caps between them, though Vaughan said he was excited.
"I'm leading a new attack into a Test match," said Vaughan.
"It's quite inexperienced but they have enough talent to take them through and put the New Zealand batsmen under pressure.
"The selection was purely on gut instinct - I guess we'll find out in five days time, but we feel we have made the tough call but the right call for this game."
Michael Vaughan (captain), Alastair Cook, Andrew Strauss, Kevin Pietersen, Ian Bell, Paul Collingwood, Tim Ambrose (wk), Stuart Broad, Ryan Sidebottom, James Anderson and Monty Panesar.