Democratic Assemblyman Herb Conaway, who is also a physician, recently introduced the legislation. It was approved Monday by the state Assembly's Health and Senior Services Committee and now heads to the Appropriations Committee for further consideration.
He said, the cooling effect of menthol allows smokers to draw more toxic substances into their lungs and hold them there.
Opponents say the ban would cost small retailers millions of dollars in lost sales and hurt state coffers.
The measure would amend existing state law that bans the sale of flavored cigarettes.
A food retailers' group says menthol cigarettes account for 35 percent to 40 percent of their total sales.