Yes and no.

Technically we don't. We have a Minister of State with responsibility for Public Health, Well Being and National Drugs Strategy.

Commonly referred to as a 'junior minister'. They exist dur to a constitutional limit on how many ministers we can have. The idea is they can focus on specific areas under the wider ministry, health in this case.

Some have been quite good IMO, law reform had been busy. Drugs however, not so much.