Summary: We classify real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadrics \(Q^{\ast,m}=\mathrm{SO}_{2,m}^o/\mathrm{SO}_m\mathrm{SO}_2\), \(m\geq 3\). We show that \(m\) is even, say \(m=2k\), and any such hypersurface becomes an open part of a tube around a \(k\)-dimensional complex hyperbolic space \(\mathbb CH^k\) which is embedded canonically in \(Q^{\ast 2k}\) as a totally geodesic complex submanifold or a horosphere whose center at infinity is \(\mathfrak A\)-isotropic singular. As a consequence of the result, we get the nonexistence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex quadrics \(Q^{\ast 2k+1}\), \(k\geq 1\).