Left-arm spinner Vettori was expected to play for the Northern Districts (Northern Knights) in the qualifying stages of the tournament along with Mumbai Indians, South Express and Lahore Lions.
"I really love playing for ND and to do so on a world stage would have been a real highlight," Vettori was quoted as saying in a press release.
The Northern Districts chief executive Peter Roachsaid that they are in the process of seeking a replacement for Vettori, through the technical committee.
"There's no guarantee, but we think Dan's exceptional circumstances should be viewed favourably," Roach said.
Northerns are already without star all-rounder Corey Anderson, who chose to represent his IPL franchise Mumbai Indians in the tournament.

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