Recent exploration has revealed extensive geological evidence for a water-rich past in the shallow subsurface of Mars. Images of in situ and loose accumulations of abundant, haematite-rich spherical balls from the Mars Exploration Rover 'Opportunity' landing site at Meridiani Planum bear a striking resemblance to diagenetic (post-depositional), haematite-cemented concretions found in the Jurassic Navajo Sandstone of southern Utah. Here we compare the spherical concretions imaged on Mars to these terrestrial concretions, and investigate the implications for analogous groundwater-related formation mechanisms. The morphology, character and distribution of Navajo haematite concretions allow us to infer host-rock properties and fluid processes necessary for similar features to develop on Mars. We conclude that the formation of such spherical haematite concretions requires the presence of a permeable host rock, groundwater flow and a chemical reaction front.