It is well-known that the Riemannian geometry of the moduli space of Euclidean SU(2)-monopoles of charge $k$ is determined by spectral curves of monopoles. I had often wondered whether there is a purely differential-geometric explanation of this fact, i.e. whether there exists an infinitesimal object on the moduli space which makes it so. I shall show that the answer is yes, and that the object in question is what I call a hyper-Poisson bivector, i.e. a bivector which induces, for each complex structure, a Poisson structure on holomorphic functions, compatible with the respective complex-symplectic form.