Minors are prohibited from smoking cigarettes.

Literal

Minors [topic-は] cigarettes [object-を] smoke thing [object-を] are-prohibited.

The nominalized verb phrase たばこを吸うのを ('the act of smoking cigarettes') is treated as the thing prohibited. The の here is the colloquial nominalizer (broadly equivalent to こと in this slot) that lets a verb phrase function as a noun and become a grammatical object. Common in formal prohibitions and rules.