Computational cannula microscopy (CCM) is a high-resolution widefield fluorescence imaging approach deep inside tissue, which is minimally invasive. Rather than using conventional lenses, a surgical cannula acts as a lightpipe for both excitation and fluorescence emission, where computational methods are used for image visualization. Here, we enhance CCM with artificial neural networks to enable 3D imaging of cultured neurons and fluorescent beads, the latter inside a volumetric phantom. We experimentally demonstrate transverse resolution of ∼6µm, field of view ∼200µm and axial sectioning of ∼50µm for depths down to ∼700µm, all achieved with computation time of ∼3ms/frame on a desktop computer.