We have analysed the Fermi Large Area Telescope (LAT) data on the SNR G73.9+0.9. We have confirmed a previous detection of high-energy gamma-rays from this source at a high significance of similar or equal to 12 sigma. The observed spectrum shows a significant curvature, peaking in EFE at similar to 1 GeV. We have also calculated the flux upper limits in the mm-wavelength and X-ray ranges from Planck and XMM-Newton, respectively. We have inspected the intensity of the CO (1 -> 0) emission line and found a large peak at a velocity range corresponding to the previously estimated source distance of similar to 4 kpc, which may indicate an association between a molecular cloud and the supernova remnant (SNR). The gamma-ray emission appears due to interaction of accelerated particles within the SNR with the matter of the cloud. The most likely radiative process responsible for the gamma-ray emission is decay of neutral pions produced in ion-ion collisions. While a dominant leptonic origin of this emission can be ruled out, the relativistic electron population related to the observed radio flux will necessarily lead to a certain level of bremsstrahlung gamma-ray emission. Based on this broad-band modelling, we have developed a method to estimate the magnetic field, yielding B greater than or similar to 80 mu G at our best estimate of the molecular cloud density (or less at a lower density). G73.9+0.9 appears similar, though somewhat weaker, to other SNRs interacting with a local dense medium detected by the LAT.