We have investigated the shape of the extinction curve in the infrared up to ~25μm for the Orion A star-forming complex. The basis of this work is near-infrared data acquired with the Visual and Infrared Survey Telescope for Astronomy, in combination with Pan-STARRS and mid-infrared Spitzer photometry. We obtain colour excess ratios for eight passbands by fitting a series of colour-colour diagrams. The fits are performed using Markov chain Monte Carlo methods, together with a linear model under a Bayesian formalism. The resulting colour excess ratios are directly interpreted as a measure of the extinction law. We show that the Orion A molecular cloud is characterized by flat mid-infrared extinction, similar to many other recently studied sightlines. Moreover, we find statistically significant evidence that the extinction law from ~1μm to at least ~6μm varies across the cloud. In particular, we find a gradient along galactic longitude, where regions near the Orion Nebula Cluster show a different extinction law compared to L1641 and L1647, the low-mass star-forming sites in the cloud complex. These variations are of the order of only 3% and are most likely caused by the influence of the massive stars on their surrounding medium. While the observed general trends in our measurements are in agreement with model predictions, both well-established and new dust grain models are not able to fully reproduce our infrared extinction curve. We also present a new extinction map featuring a resolution of 1′ and revisit the correlation between extinction and dust optical depth. This analysis shows that cloud substructure, which is not sampled by background sources, affects the conversion factor between these two measures. In conclusion, we argue that specific characteristics of the infrared extinction law are still not well understood, but Orion A can serve as an unbiased template for future studies.