We report the spontaneous and rapid growth of micrometre-scale tubes from crystals of a metal oxide-based inorganic solid when they are immersed in an aqueous solution containing a low concentration of an organic cation. A membrane immediately forms around the crystal, and this membrane then forms micrometre-scale tubes that grow with vast aspect ratios at controllable rates along the surface on which the crystal is placed. The tubes are composed of an amorphous mixture of polyoxometalate-based anions and organic cations. It is possible for liquid to flow through the tubes, and for the direction of growth and the overall tube diameter to be controlled. We demonstrate that tube growth is driven by osmotic pressure within the membrane sack around the crystal, which ruptures to release the pressure. These robust, self-growing, micrometre-scale tubes offer opportunities in many areas, including the growth of microfluidic devices and the self-assembly of metal oxide-based semipermeable membranes for diverse applications.