Subsurface processes can be simulated at multiple scales with variable degrees of fidelity. Some microscopic (pore-scale) features of reactive transport cannot be properly resolved in macroscopic (Darcy-scale) models. While microscopic descriptors might be closer to reality, they are computationally unfeasible when deployed on a macroscale. Hybrid algorithms combine the physical fidelity of a microscopic model with the computational efficiency of its macroscopic counterpart. We develop a hybrid model of dynamic reactive fronts in an open fracture, with a chemical reaction occurring in the zone of contact between two dissolved species. Away from the front, both fluid flow and solute transport are described by one-dimensional models. In the front's proximity, two-dimensional Stokes equations are used to model fluid flow and solute transport is described with advection-diffusion-reaction equations. These two descriptors are coupled via an iterative procedure, which enforces the continuity of concentrations and mass fluxes across the interface between the two models. Our numerical experiments demonstrate that the hybrid model outperforms its microscopic and macroscopic counterparts in terms of computational time and representational accuracy, respectively.