The motion, bearing the signatures of 31 MPs, was ruled in order by the speaker of parliament ahead of a sitting on Friday afternoon, Radio New Zealand reported.
The government spent last week shoring up its support, swearing in a new Health Minister, Jerome Ludvunae, and creating two new under-secretary positions.
It said it was confident of its majority support, with about 30 MPs in the 52-member parliament - but observers say some MPs are almost certain to have defected.
Nevertheless, the motion is a setback for the government's promise to try and bring stability to a political system plagued by frequent motions and changes of government, Radio New Zealand reported.
Salwai's government was created after snap elections in January after half the previous government was jailed for corruption, related to payments offered for support in a previous motion.