Density functional theory calculations using the pseudopotential-plane-wave approach are employed to investigate the structural and magnetic properties of epitaxial CrAs thin films on GaAs(001). Motivated by recent reports of ferromagnetism in this system, we compare zinc-blende CrAs films (continuing the lattice structure of the GaAs substrate) and CrAs films with a bulklike orthorhombic structure epitaxially matched to three units of the GaAs(001) lattice. We find that even for very thin films with three Cr layers the bulklike crystal structure is energetically more favorable than zinc-blende CrAs on GaAs(001). CrAs films with orthorhombic structure, even if under epitaxial strain, preserve the antiferromagnetic order of CrAs bulk. In the light of our calculations, it appears likely that the magnetic hysteresis loop measured in ultrathin CrAs/GaAs(001) films originates from uncompensated antiferromagnetic moments near the CrAs/GaAs interface. In conclusion, our results do not support earlier proposals that thick CrAs films could be employed as perfectly matched spin-injection electrode on GaAs.