She waved at me.

Literal

She [topic-は] me [to-に] hand [object-を] shook.

手を振る — literally 'to shake the hand' — is the standard verb collocation for waving. The body part is marked as the direct object with を, even though English would render it adverbially ('waved her hand'). This noun-を-verb pattern is everywhere in Japanese body-action vocabulary: 首を振る ('shake one's head'), 目をつぶる ('close one's eyes'), 口を開ける ('open one's mouth'). The overall image is of a body part being moved as if it were a separate object — a structural difference from English's 'I shook my hand,' which feels redundant.