Lateral metre-scale periodic variations in porosity and composition are found in many dolomite strata. Such variations may embed important information about dolomite formation and transformation. Here we show that these variations could be fossilized chemical waves emerging from stress-mediated mineral-water interaction during sediment burial diagenesis. Under the overlying loading, crystals in higher porosity domains are subjected to a higher effective stress, causing pressure solution. The dissolved species diffuse to and precipitate in neighbouring lower porosity domains, further reducing the porosity. This positive feedback leads to lateral porosity and compositional patterning in dolomite. The pattern geometry depends on fluid flow regimes. In a diffusion-dominated case, the low- and high-porosity domains alternate spatially with no directional preference, while, in the presence of an advective flow, this alternation occurs only along the flow direction, propagating like a chemical wave. Our work provides a new perspective for interpreting diagenetic signatures in sedimentary rocks.