Whether addiction itself is a disease or not is open for debate - but the consequences of that addiction can lead to disease states.
There is a fair degree of evidence from familial studies, studies with identical twins and studies with non-identical twins to suggest that addiction can be attributed at least in part to a hardwired biological imperative, so the latest thinking on addiction is that it is part genetic predisposition, part exposure to addictive substances.
And if something is part genetic predispostion, part nature - such as some forms of heart disease, or cancer, and if they can be treated and classified as a disease, then its does not seem a great stretch to describe addiction that way either.
And in terms of treating the addiction, is it better to treat it as a medical issue, a disease, or as a social/ cultural issue?