Abstract Recent analyses of the cosmic microwave background (CMB) and the Lyman-α forest indicate a mild preference for a deviation from a power law primordial matter power spectrum (a so-called ‘running’). We introduce an extension to the BAHAMAS suite of simulations to explore the effects that a running scalar spectral index has on large-scale structure (LSS), using Planck CMB constraints to initialize the simulations. We focus on 5 key statistics: i) the non-linear matter power spectrum ii) the halo mass function; iii) the halo two-point auto correlation function; iv) total mass halo density profiles; and v) the halo concentration-mass relation. We find that the matter power spectrum in a Planck-constrained running cosmology is affected on all k −scales examined in this study. These effects on the matter power spectrum should be detectable with upcoming surveys such as LSST and Euclid. A positive running cosmology leads to an increase in the mass of galaxy groups and clusters, with the favoured negative running leading to a decrease in mass of lower-mass (M ≲ 1013M⊙) haloes, but an increase for the most massive (M ≳ 1013M⊙) haloes. Changes in the mass are generally confined to 5-$10\%$ which, while not insignificant, cannot by itself reconcile the claimed tension between the primary CMB and cluster number counts.We also demonstrate that the observed effects on LSS due to a running scalar spectral index are separable from those of baryonic effects to typically a few percent precision.