Southee is expecting the birth of his child.
The other notable additions to the squad include uncapped wicketkeeper Tom Blundell, who is set to make his debut replacing injured B.J. Watling along with batsman George Worker.
"Obviously there are things more important than cricket and we support Tim and his decision to stay with his family right now," Black Caps selector Gavin Larsen said.
"George will join the Test squad for the first time on the back of his form in first class cricket over the past couple of seasons."
Worker has not yet represented New Zealand in Tests, but has played six limited overs international matches. He made his debut in a T20 International against Zimbabwe in October 2015.
First Published: November 29, 2017, 4:08 PM IST