Microbeam facilities provide a unique opportunity to investigate the effects of ionising radiation on living biological cells with a precise control of the delivered dose. This paper describes dosimetry calculations performed at the single-cell level in the microbeam irradiation facility available at the Centre d'Etudes Nucléaires de Bordeaux-Gradignan in France, using the object-oriented Geant4 Monte Carlo simulation toolkit. The cell geometry model is based on high-resolution three-dimensional voxelised phantoms of a human keratinocyte (HaCaT) cell line. Such phantoms are built from confocal microscopy imaging and from ion beam chemical elemental analysis. Results are presented for single-cell irradiation with 3 MeV incident alpha particles.