Microtubules are dynamic filaments that assemble spindles for eukaryotic cell division. As the concentration profiles of soluble tubulin and regulatory proteins are non-uniform during spindle assembly, we asked if diffusiophoresis - motion of particles under solute gradients - can act as a motorless transport mechanism for microtubules. We identify the migration of stable microtubules along cytoplasmic and higher concentration gradients of soluble tubulin, MgCl, Mg-ATP, Mg-GTP, and RanGTP at speeds O(100) nm/s, validating the diffusiophoresis hypothesis. Using two buffers (BRB80 and CSF-XB), microtubule behavior under MgCl gradients is compared with negatively charged particles and analyzed with a multi-ion diffusiophoresis and diffusioosmosis model. Microtubule diffusiophoresis under gradients of tubulin and RanGTP is also compared with the charged particles and analyzed with a non-electrolyte diffusiophoresis model. Further, we find that tubulin and RanGTP display concentration dependent cross-diffusion that influences microtubule diffusiophoresis. Finally, using Xenopus laevis egg extract, we show that diffusiophoretic transport occurs in an active cytoplasmic environment.