Intravoxel incoherent motion (IVIM) imaging is increasingly recognised as an important tool in clinical MRI, where tissue perfusion and diffusion information can aid disease diagnosis, monitoring of patient recovery, and treatment outcome assessment. Currently, the discovery of biomarkers based on IVIM imaging, similar to other medical imaging modalities, is dependent on long preclinical and clinical validation pathways to link observable markers derived from images with the underlying pathophysiological mechanisms. To speed up this process, virtual IVIM imaging is proposed. This approach provides an efficient virtual imaging tool to design, evaluate, and optimise novel approaches for IVIM imaging. In this work, virtual IVIM imaging is developed through a new finite element solver, SpinDoctor-IVIM, which extends SpinDoctor, a diffusion MRI simulation toolbox. SpinDoctor-IVIM simulates IVIM imaging signals by solving the generalised Bloch-Torrey partial differential equation. The input velocity to SpinDoctor-IVIM is computed using HemeLB, an established Lattice Boltzmann blood flow simulator. Contrary to previous approaches, SpinDoctor-IVIM accounts for volumetric microvasculature during blood flow simulations, incorporates diffusion phenomena in the intravascular space, and accounts for the permeability between the intravascular and extravascular spaces. The above-mentioned features of the proposed framework are illustrated with simulations on a realistic microvasculature model.