The National Secular Society (NSS) says the drink is bad for society because of its many links to antisocial behaviour, adding it's unfair the millions the trust makes from the drink are not taxed because of its charitable status.
The Charity Commission is investigating whether claims that the monastery is 'abusing the charitable system' are valid.
Stephen Evans, NSS campaigns director, commented: "Charitable status and the accompanying tax benefits should only be granted to organisations that deliver a demonstrable public benefit.
"In the case of Buckfast Abbey, the social harm caused appears to outweigh any public good. Where this happens, or where the good is simply not good enough, public confidence in supporting charities risks being undermined".
According to the commission, Buckfast Abbey Trust garnered £8.8 million between 2014 and 2015 - most of the income was from the wine.
The commission also says the religious organisation helps the public by providing human resources, services and facilities.
According to The Telegraph, last year Buckfast Abbey Trust said: "The majority of people who drink the tonic wine do so responsibly. We fully support the efforts of charities such as Drinkaware who work to reduce alcohol misuse and harm in the UK."