Boult suffered the hand injury on day three of New Zealand’s Second Test against Australia at the MCG, when struck by a Mitchell Starc delivery.
The Black Caps were way off the pace at stumps on day three in Melbourne, with Australia on 4-137 in their second dig, leading by 456 runs overall.
Boult, who was bowled by Starc for 8, was struck on his non-bowling hand as New Zealand were skittled for 148 in their first innings.
The left-armer was in discomfort following the blow but did bowl in the second innings, getting through nine overs.
He went for scans during the tea break which confirmed the hand fracture and ruled him out of the Third Test in Sydney from January 3.
“It’s obviously gutting news for Trent and our group,” opener Tom Latham said.
It’s understood Boult will be out for four weeks, with a replacement player for the Third Test to be named following the MCG match.
Matt Henry is likely to come into the side for Sydney. New Zealand already lost quick Lockie Ferguson to a calf injury in his debut in Perth.
Boult missed that Test match due to a side strain but was declared fit for the Second Test.
Rotorua-born 30-year-old Boult is fourth on New Zealand’s all-time Test wicket-takers list with 256 scalps.