The invariant differential cross section of inclusive ω(782) meson production at midrapidity (| y| < 0.5) in pp collisions at s=7TeV was measured with the ALICE detector at the LHC over a transverse momentum range of 2<pT<17GeV/c. The ω meson was reconstructed via its ω→ π⁺π^-π decay channel. The measured ω production cross section is compared to various calculations: PYTHIA 8.2 Monash 2013 describes the data, while PYTHIA 8.2 Tune 4C overestimates the data by about 50%. A recent NLO calculation, which includes a model describing the fragmentation of the whole vector-meson nonet, describes the data within uncertainties below 6GeV/c, while it overestimates the data by up to 50% for higher p_T. The ω/ π ratio is in agreement with previous measurements at lower collision energies and the PYTHIA calculations. In addition, the measurement is compatible with transverse mass scaling within the measured p_T range and the ratio is constant with Cω/π0=0.67±0.03(stat)±0.04(sys) above a transverse momentum of 2.5GeV/c.