But former seamer Mark Gillespie returns along with leg-spinner Tarun Nethula, for the second test starting in Hamilton on Thursday.
National Selection Manager Kim Littlejohn said Southee would need to find improved form to return to the test squad.
"Tim Southee hasn't been included. He a talented young fast bowler and we are confident he will return to the Plunket Shield and continue to put pressure on those in the Test team.
"Mark Gillespie returns to international cricket after showing good form recently and provides and strong and reliable bowling option.
"We are pleased to be able to offer Tarun an opportunity. He is bowling well and offers a point of difference to the attack.
"BJ Watling and Dean Brownlie were not considered for selection as they have not recovered sufficiently from injury."
The squad will assemble in Hamilton tomorrow morning.
Squad: Ross Taylor, Brent Arnel, Trent Boult, Doug Bracewell, Andrew Ellis, Mark Gillespie, Martin Guptill, Chris Martin, Brendon McCullum, Tarun Nethula, Rob Nicol, Kruger Van Wyk, Daniel Vettori, Kane Williamson.
