(My answer to this question at Quora.com)
Most definitely Hebrew—of a comparatively late (i.e. 7th to 6th-century BCE) vintage i.e. a good hundred or two hundred years before the Classical Greek period.
Its rich poetic quality precludes the possibility that it is a translation, and only its contemplative “wisdom literature” philosophy and its setting (somewhere outside the Holy Land), and its use of foreign-sounding words or forms, suggest that it may have been composed during the Babylonian exile.
The Greek translation (Septuagint) of the book was produced around 200 BCE.