The photoproduction of ω mesons on LH₂, C and Nb has been measured for incident photon energies from 900 to 1300 MeV using the CB/TAPS detector at ELSA. The ω line shape does not show any significant difference between the LH₂ and the Nb targets. The experiment was motivated by transport calculations that predicted a sensitivity of the ω line shape to in-medium modifications near the production threshold on a free nucleon of E_γ^lab  = 1109 MeV. A comparison with recent calculations is given.