Organisers confirmed the screening would go ahead, with Incredibly Strange programmer Ant Timpson paying tribute to Yelchin before the film starts.
Timpson, who didn't know Yelchin, said the best way to honour the actor was to celebrate their legacy.
"Much like James Dean, Paul Walker, gifted actors who also died in car accidents, Anton Yelchin's sudden death has left us sad and fumbling," Timpson said.
"This morning there was discussion regarding whether it would be inappropriate to go ahead with the screening.
"As a programmer, I truly feel that the best way to acknowledge an actors sudden passing is to celebrate their talent and to showcase what they loved doing."
Green Room will screen as part of the NZIFF, which kicks off in Auckland on July 20. It also stars Patrick Stewart and Imogen Poots.
Yelchin's next film is Star Trek Beyond, due to debut in July.