Liberal John Ames introduced the motion, which calls Williamson's comments racially charged.
The political website iPolitics reported that Williamson told delegates at a conference in Ottawa that it makes no sense to pay "whities" to stay home while companies bring in "brown people" as temporary foreign workers.
The Conservative MP, who represents New Brunswick Southwest, apologized in tweets Saturday for the language he used in talking about the temporary foreign workers program.
His remarks have also prompted criticism from within his own Tory caucus.
The motion in New Brunswick is expected to come up for debate within the next week.