The Permanent Committee said:
“After the Committee for Verdicts studied the issue, they answered that it is not allowed to use medicine mixed with intoxicants to rinse and clean the mouth and teeth or for disinfection due to the presence of permissible and available substitutes which can take its place and are free from that [i.e. alcohol]”
There are many alcohol-free mouthwashes available on the market today. An example is Listerine Zero.
Faisal Ibn Abdul Qaadir Ibn Hassan