Santner suffered discomfort during the limited overs matches against England and had a scan, which revealed a bone defect. Further scans showed the injury had deteriorated and needed surgery that would keep him out for between six and nine months.
"On a personal level everyone feels for Mitchell," New Zealand coach Mike Hesson said in a statement. "He's a popular guy in the changing room and he's well respected for the work he puts in for the side.
"Mitchell is a key player in all three formats for us, so we'll certainly miss him in the upcoming series.
"It's important though that he gets this fixed and we have him back for what is a big next 18 months for us."
Leg-spinner Todd Astle has been brought in as a replacement for the test series, which starts on March 22 in Auckland with New Zealand's first day-night test.
"Having another spin bowling all-rounder in Todd is of real benefit for us and he'll be looking forward to his opportunity," New Zealand selector Gavin Larsen said.
"Being involved in the first day-night test in New Zealand is really exciting and there's always something special about playing England.
"They have match winners throughout their squad so we expect a challenging series."
Regular test wicketkeeper BJ Watling has also returned to the side after recovering from a hip injury.
Watling had played several games for his first class side as a batsman only as he slowly worked his way back to fitness.
Tom Blundell, who replaced Watling and scored a century on debut against West Indies last December, has dropped out of the squad.
"BJ is a proven performer at test level for us and brings a lot to the group both on and off the field," Larsen added.
"We've monitored BJ's progress over the past few months and it's great to see him back with the gloves for Northern Districts.
"Tom Blundell did a great job in BJ's absence and we'll keep working with him going forward."
New Zealand test squad: Kane Williamson (captain), Todd Astle, Trent Boult, Colin de Grandhomme, Matt Henry, Tom Latham, Henry Nicholls, Jeet Raval, Tim Southee, Ross Taylor, Neil Wagner, BJ Watling.
(Reporting by Greg Stutchbury; Editing by Toby Davis)
