  We consider a Yang-Mills-Higgs theory with gauge group $G=SU(n)$ broken to
$G_{v} = [SU(p)\times SU(n-p)\times U(1)]/Z$ by a Higgs field in the adjoint
representation. We obtain monopole solutions whose magnetic field is not in the
Cartan Subalgebra. Since their magnetic field vanishes in the direction of the
generator of the electromagnetic group $U(1)_{em}$, we call them Dark
Monopoles. These Dark Monopoles must exist in some Grand Unified Theories
(GUTs) without the need to introduce a dark sector. We analyze the particular
case of $SU(5)$ GUT, where we obtain that their mass is $M = 4\pi v
\widetilde{E}(\lambda/e^{2})/e$, where $\widetilde{E}(\lambda/e^{2})$ is a
monotonically increasing function of $\lambda/e^{2}$ with
$\widetilde{E}(0)=1.294$ and $\widetilde{E}(\infty)=3.262.$ We also give a
geometrical interpretation to their non-abelian magnetic charge.
