The law is set to come into effect on Sunday.
Imperial Tobacco Canada issued a news release on Thursday saying the province exceeded its legal authority with the ban.
It says there is a lack of evidence demonstrating the flavoured products with menthol are attractive to youth.
Rob Cunningham, a lawyer with the Canadian Cancer Society, dismissed the legal challenge before the Nova Scotia Supreme Court as a last-minute public relations campaign, adding there is strong evidence that young people are using the products being banned.
He praised the Nova Scotia government for adopting the ban on menthol, adding it will help other provinces follow a similar path.
Dr. Robert Strang, the province's chief medical officer, said in an interview the province has no intention of backing away from its law due to the legal challenge.
"We're absolutely confident in the rationale and the strength of our legislation. This is not going to distract us ... We'll deal with any legal challenges over time," he said.
The Alberta NDP has been in favour of a menthol ban and Premier Rachel Notley has said she expects there will be an announcement in the coming days.