Garzón is a member of the Unidas Podemos political party which formed a coalition government with the Socialist Party in January.
In its election campaign, the party vowed to protect youth and addicts from the dangers of gambling.
Under the proposed laws, TV gambling advertising will be reduced by as much as 80% and gambling companies will be banned from hiring celebrities to market their products.
Another proposed law will prevent football clubs from selling their shirts to children if they are sponsored by a gambling company.
Garzón said: “The regulation has to be similar to tobacco. We are not regulating the textile sector here, but a sector that has an impact on public health.”
In November last year, Spain’s online gambling operators agreed to a voluntary advertising code as the government threatened to impose tighter restrictions.
The voluntary code included the addition of responsible gambling messaging in all advertisements and a ban on depictions of famous athletes participating in gambling.
Garzón’s new suggested laws will be discussed by the cabinet before being put to parliament.
