She quickly tucked the money out of sight.

Literal

She [topic-は] cannot-be-seen place [in-に] swiftly money [object-を] placed.

見えない is the negative of 見える ('to be visible / can be seen'), and crucially this is the spontaneous-perception verb, not the volitional potential 見られる ('can look at deliberately'). 見えないところ — 'a place that isn't visible' — is a relative clause modifying ところ; the implied subject is whatever's being placed there (the money), not the woman. すばやく is the adverbial form of すばやい ('swift, quick'); the sentence mixes that into a compact, slightly furtive scene.