Black hole accretion disks appear to produce invariably plasma outflows that result in blue-shifted absorption features in their spectra1. The X-ray absorption-line properties of these outflows are quite diverse, ranging in velocity from non-relativistic2 (~ 300 km/sec) to sub-relativistic3 (~ 0.1c where c is the speed of light) and a similarly broad range in the ionization states of the wind plasma2,4. We report here that semi-analytic, self-similar magnetohydrodynamic (MHD) wind models that have successfully accounted for the X-ray absorber properties of supermassive black holes5,6, also fit well the high-resolution X-ray spectrum of the accreting stellar-mass black hole, GRO J1655-40. This provides an explicit theoretical argument of their MHD origin (aligned with earlier observational claims)7 and supports the notion of a universal magnetic structure of the observed winds across all known black hole sizes.