Labour’s Roisin Shortall has said the link needs to be broken between sport and the promotion of alcohol.
Speaking on RTÉ's News at One, Ms Shortall said a difficulty lies in the return alcohol industries receive in sponsoring sports events.
She said alcohol industries have access to promotional opportunities and marketing which then promotes excessive drinking, especially amongst young people.
The Irish Rugby Fooball Union has said the withdrawal of sponsorship by drinks companies of sporting events would leave a gap in revenue that could not be replaced.
Speaking On RTÉ's Morning Ireland, Philip Browne of the IRFU criticised the Department of Health for failing to work with sporting organisations.
Media reports suggest that new legislative proposals circulated in Government by Minister of State Alex White would outlaw all drink sponsorship of large sports events by 2020 and ban new sponsorship contracts from 2016.
It is understood arts and cultural festivals would be exempt from the ban.
Ms Shortall said she believed the phasing out of such sponsorship by 2020 was reasonable, saying it would allow sports organisations to find alternative sponsors.
Minister of Sport Leo Varadkar has described the issue of alcohol sponsorship as "complicated".
It is understood the laws proposed in a Department of Health memo, would prevent the sponsorship of large sporting fixtures, but would not apply to arts and cultural events.