Hidden sectors are a generic prediction of string theory compactifications and result in a promising landscape for dark matter model building. We consider the case of hidden sector magnetic monopoles produced via a thermal phase transition in the early Universe and subsequently diluted by pair annihilation. We show that for symmetry-breaking scales $\gtrsim 100\mathrm{\text{PeV}}$, the monopole abundance is unacceptably high, overclosing the Universe. Our bounds are robust against variations in the initial fraction of energy density deposited in the hidden sector, exhibiting only a weak power-law dependence on this quantity. The bound is substantially tightened in the case of multiple hidden sectors. The standard cosmology may only be recovered if one of the following is true: the hidden sector(s) are non-existent, the hidden sectors have no monopoles with symmetry-breaking scale above 100 PeV, the maximum temperature of each monopole-producing hidden sector after reheating is below its symmetry-breaking scale, or the monopole abundance is diluted by an additional physical mechanism (such as early matter domination, the Langacker-Pi mechanism, or capture by primordial black holes).