We report molecular line observations in the CO J=3→2, 6→5 and 7→6 transitions, made using the Atacama Pathfinder Experiment Telescope (APEX), toward the massive and dense core IRAS 16562−3959. This core harbors a string of radio sources thought to be powered by a central collimated jet of ionized gas. The molecular observations show the presence of high velocity gas exhibiting a quadrupolar morphology, most likely produced by the presence of two collimated outflows. The southeast-northwest molecular outflow is aligned with the string of radio continuum sources, suggesting it is driven by the jet. We find that the excitation temperature of the gas in the SE-NW outflow is high, with values of 145 and 120 K for the blueshifted and redshifted lobes, respectively. This outflow has a total mass of 1.92 \Msun, a total momentum of ∼89 \Msun \kms and an averaged momentum rate of ∼3.0×10−2 \Msun \kms yr−1, values characteristics of flows driven by young massive stellar objects with high luminosities (Lbol∼2×104 \Lsun). Complementary data taken with the Atacama Submillimeter Telescope Experiment (ASTE) in high density and shock tracers support the picture that IRAS 16562−3959 is an accreting young massive star associated with an ionized jet, which is the energy source of a molecular outflow.FONDAPFONDAP