The decision came shortly after George Washington University professor Jonathan Turley, in a letter on on his website, told Idaho officials he planned to sue on behalf of the producer of Five Wives Vodka.
He called the ban unconstitutional and gave the state 10 days to reverse its position.
Idaho State Liquor Division director Jeff Anderson said last month that the brand is offensive to Mormons who make up more than a quarter of Idaho's population and would not be sold in the state. The Mormon Church at one time allowed polygamy but abandoned the practice in 1890.
Anderson did not immediately respond to a request for comment Wednesday.
"Idaho is the only state to raise religious and social sensibilities as a basis to deny entry to this product," Turley wrote in his letter.
He said that a lawsuit would raise issues of free speech and other claims.
Idaho had defended its decision not to allow Five Wives Vodka, saying state liquor stores already make hundreds of vodka brands available for sale and don't have room for another brand priced at around $20 a bottle.
Five Wives Vodka is available in Utah and Wyoming and will soon be sold in Montana, Colorado and other states.
A spokesman for Five Wives Vodka, Steve Conlin, said Wednesday that the company wasn't seeking to make fun of anyone with its brand name, though it knew people would make the association with polygamy. He said the company would sue Idaho on principle if necessary.
"They shouldn't be able to ban a product based on its packaging without substantial reasoning," he said.
Conlin said Turley and a number of attorneys contacted the company last week, and "after reading Turley's blog on the subject and chatting with him over the weekend, we decided we would move forward with some sort of legal action.''
Conlin said that proceeds from Five Wives T-shirt sales would pay ``a large portion'' of Turley's legal fees.
The vodka label depicts five turn-of-the-20th-century women dressed in undergarments holding strategically placed kittens over their genitalia.
Ogden Distillery owner Tim Smith said the label is from a old photo he found on the Internet and used it with no information on its origins or the five women depicted. Tribune research later revealed the image is of the Barrison Sisters, who toured the United States and Europe as hit vaudeville performers between 1890 and 1910.
In their cat dance, the performers raised their skirts revealing their underwear each with a live kitten secured over the crotch, according to news accounts.
Turley has been involved in a lawsuit involving polygamy before. He represents the family of Kody Brown, a star of the reality TV show "Sister Wives," which follows Brown and his four wives. Brown, a former Utah resident, had sued in Utah, claiming the state's bigamy statute violates the family's constitutional rights.