The bill was not passed due to concern about the spread of rabies.
It received 44 votes but bill need a constitutional majority of 50 to pass the chamber.
The bill was sponsored by Representative Jeremy Faison, R-Cosby, who argued that rabies has not been a problem with pet skunks in other states.
The law would have allowed for only domesticated skunks who have had their glands removed so they could not spray.
Faison said skunks kept as pets normally have their scent glands removed at an early age.
Skunks can be sold as pets for as much as $1,000 each and there could be possible revenue for those eager to engage in skunk marketing.