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Latham, who was stand-in captain for the test at the Sydney Cricket Ground, suffered a fracture when taking the final catch before the Australian declaration on day four.
The opener went out to bat but lasted just 15 balls before he was adjudged lbw by Mitchell Starc for one.
Latham should be fit for the two-test series against India starting in late February and is targeting a return during the three-match ODI series.
Coach Gary Stead has also provided injury updates on squad members who played in the 3-0 series defeat in Australia.
"Lockie Ferguson (right calf-strain) has returned to running and performing bowling drills. He'll continue to progress over the next couple of weeks with the potential to return to domestic cricket early next month," he said.
"Trent Boult has been resting his broken right-hand and will return to bowling later this week. He'll be touch-and-go to be available for the Indian T20 series later this month and we'll continue to monitor him closely over the next few weeks.
"Matt Henry has had his broken left-thumb splinted and will require around a month for it to fully heal. In this time he will still be able to practise bowling and will look at a return to play early next month.
Stead also confirmed that Kane Williamson, Henry Nicholls and Mitchell Santner, who all missed the third test due to illness, had the flu.
"Kane, Henry and Mitch are regaining their health after being struck down with Influenza A and will continue be monitored as they slowly rebuild their strength and fitness."
The Black Caps T20 squad to face India will be named late next week. The first match is in Auckland on January 24.