Vertical arrays of crystalline zinc oxide (ZnO) nanowires grown on various substrates find applications in dye-sensitized and hybrid organic/inorganic bulk-heterojunction solar cells. The ability to grow dense nanowires at high rates and the fundamental understanding of the growth process are important for these applications. Herein, we show that heterogeneous growth of ZnO nanowires on substrates seeded with ZnO nanoparticles in an aqueous solution of methenamine and zinc nitrate is mass transport limited. Mass transport limited growth leads to an inverse relationship between the nanowire dimensions (height and diameter) and the nanowire number density. This mass transport limitation also leads to nonuniform growth near the boundaries between seeded and unseeded regions. Stirring the reaction solution increases the nanowire growth rate. Experimental results were interpreted within the framework of two simple but nontrivial models of the solution phase species transport and the nanowire growth. Additionally, it was determined that the anisotropic growth is due to the intrinsic growth kinetics of the (101̄0) and (0001) surfaces of ZnO in zinc nitrate and methenamine and not due to the growth process being mass transport limited as previously suggested.