We present a measurement of the transverse momentum distribution of Z bosons produced in p&pmacr; collisions at sqrt[s] = 1.8 TeV from data collected by the DO experiment at the Fermilab Tevatron Collider. We find good agreement between our results and current resummation calculations, and also use our data to extract nonperturbative parameters for a particular version of the resummation formalism. The resulting values are significantly more precise than obtained in previous determinations.