On his state-wide 'Vikas Samiksha Yatra', Kumar told the people in Bakhri village of Sitamarhi district that those who report cases of violation of the alcohol ban to authorities would be protected, and also urged them to remain vigilant.
The identity of the complainant would remain secret, he said.
Banning the sale and consumption of alcohol - domestic and Indian Made Foreign Liquor - has been an issue close to Kumar. It was also one of his major poll campaign promises.
Kumar said the total prohibition was imposed on citizens' demand. He exhorted women and youth to join the government's efforts against the sale and consumption of alcohol.
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"The radical step of banning sale and consumption of alcohol was taken in view of a strong demand from women. It has brought about a positive change in the society but at the same time, for many people, illegal sale of liquor has become a lucrative business," Kumar said.
He said a separate wing of police dedicated to ensure proper implementation has been set up and also a helpline has been created for reporting cases of violation.
The chief minister urged women and youth to educate alcoholics about the ill-effects of liquor consumption.
The implementation of the liquor ban in Bihar has drawn critical remarks from the main opposition RJD and others.
Hindustani Awam Morcha leader and former chief minister Jitan Ram Manjhi has alleged that only the poor were targeted for violations of prohibition while the better-off, including senior government officials, continued to enjoy their drink with impunity.
The JD(U) has denied the charges. It has claimed that following prohibition, there has been a drop in crime rates, road accidents and improvement in the quality of life.