Te Rangi and Henry would normally be among the contenders for the 24-man squad, with Te Rangi a strong chance for the final squad.
The Tall Blacks will hold a camp early next month before hosting Korea in three internationals. An extended squad will then depart on July 26 for a series of games in Korea, China, Lithuania and Serbia before the World Cup starts in Spain at the end of August. New Zealand have been drawn in the same pool as the United States, Dominican Republic, Finland, Turkey and Ukraine.
Te Rangi, Henry and Ili have already seen their one-year contracts terminated by the Southland Sharks.
NBL chairman Sam Rossiter-Stead said Sharks management "acted swiftly and decisively and we fully endorse their decision to suspend these three players with immediate effect".
The loss of the players left the Sharks so desperate, coach Paul Henare has had to come out of retirement to play. It ushered in a good run of results and if they win their next game, they are in contention for the playoffs. Henare retired from playing after the Breakers' first ANBL title in 2010.
Breakers chief executive Richard Clark said Te Rangi had let himself, his family and the club down.
"As a club, we are believers in the power of redemption, but that redemption must be earned," he said. "Reuben has made a mistake and now has the opportunity to show how he will learn and respond to this situation. The next step for Reuben is sentencing, and his future as a Breaker will be dependent on the outcome of that process."