Plants require effective vascular systems for the transport of water and dissolved molecules between distal regions. Their survival depends on the ability to transport sugars from the leaves where they are produced to sites of active growth; a flow driven, according to the Münch hypothesis, by osmotic gradients generated by differences in sugar concentration. The length scales over which sugars are produced (Lleaf) and over which they are transported (Lstem), as well as the radius r of the cylindrical phloem cells through which the transport takes place, vary among species over several orders of magnitude; a major unsettled question is whether the Münch transport mechanism is effective over this wide range of sizes. Optimization of translocation speed predicts a scaling relation between radius r and the characteristic lengths as r ∼ (Lleaf Lstem)1/3. Direct measurements using novel in vivo techniques and biomimicking microfluidic devices support this scaling relation and provide the first quantitative support for a unified mechanism of sugar translocation in plants spanning several orders of magnitude in size. The existence of a general scaling law for phloem dimensions provides a new framework for investigating the physical principles governing the morphological diversity of plants.