The PHENIX experiment at the Relativistic Heavy Ion Collider has measured low-mass vector-meson, omega, rho, and phi, production through the dimuon decay channel at forward rapidity (1.2 < vertical bar y vertical bar < 2.2) in p + p collisions at root s = 200 GeV. The differential cross sections for these mesons are measured as a function of both p(T) and rapidity. We also report the integrated differential cross sections over 1 < p(T) < 7 GeV/c and 1.2 < vertical bar y vertical bar < 2.2: d sigma/dy(omega + rho rho -> mu mu) = 80 +/- 6(stat) +/- 12(syst)nb and d sigma/dy(phi -> mu mu) = 27 +/- 3(stat) +/- 4(syst)nb. These results are compared with midrapidity measurements and calculations.