"The onus of the WICB is to protect the integrity of international cricket at all times," the board's Director of Cricket Richard Pybus said in a statement.
"International cricket, and specifically test cricket, is priority and requires dedicated preparation which is integral to team success.
"The WICB policy requires players to commit to sufficient preparation leading in to a series as part of a culture of excellence," Pybus added.
Difficult to read and more successful in the shorter formats, Narine has played six tests claiming 21 wickets, 18 of them coming against New Zealand.
His absence would force West Indies to look at off-spinner Shane Shillingford, just back from a suspension for an illegal bowling action, and towering left-arm spinner Sulieman Benn who played his last test in December 2010.
Narine will be considered for the two Twenty20 Internationals against New Zealand in July, the WICB said.
Kingston hosts the first test from June 8, followed by matches in Port-of-Spain (June 16-20) and Guyana (June 26-30).
(Reporting by Amlan Chakraborty, Editing by Nick Mulvenney)
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