The Hebrew Bible does not prohibit a man from having more than one wife, and the way it handles the practice is more interesting than a prohibition would be: it legislates around the consequences. Deuteronomy addresses a man with two wives, one loved and one not, and forbids him to prefer the son of the loved wife when he divides the inheritance. A law of that shape assumes the arrangement and constrains its unfairness. Elsewhere the narratives report it of Abraham, Jacob, Elkanah, David and Solomon, and the tension it produces in a household, between Sarah and Hagar, between Leah and Rachel, between Hannah and Peninnah, is described at length and never resolved by a rule.
There is one clear ancient Jewish voice against it. The Damascus Document, from the Dead Sea material, condemns taking two wives in their lifetimes and cites the creation of male and female and the pairs entering the ark, which is an argument from the order of creation of exactly the kind Christianity would later make.
The rabbinic tradition permitted it and made it rarer by other means, principally the marriage contract, which made a second household expensive, and by the requirement of consent in some communities. The formal end in Ashkenaz came by enactment around the year 1000 and not by exegesis, which is itself the clearest evidence that the texts could not be made to yield a prohibition.