A new class of infinite dimensional representations of the Yangians $Y(\frak{ g})$ and $Y(\frak{ b})$ corresponding to a complex semisimple algebra $\frak{ g}$ and its Borel subalgebra $\frak{ b}\subset\frak{ g}$ is constructed. It is based on the generalization of the Drinfeld realization of $Y(\frak{ g})$, $\frak{ g}=\frak{ gl}(N)$ in terms of quantum minors to the case of an arbitrary semisimple Lie algebra $\frak{ g}$. The Poisson geometry associated with the constructed representations is described. In particular it is shown that the underlying symplectic leaves are isomorphic to the moduli spaces of $G$-monopoles defined as the components of the space of based maps of $\mathbb{ P}^1$ into the generalized flag manifold $X=G/B$. Thus the constructed representations of the Yangian may be considered as a quantization of the moduli space of the monopoles.
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