A search for the muon catalyzed fusion reaction dd → 4 He + γ in the ddµ muonic molecule was performed using the experimental µCF installation TRI-TON and N aI(T l) detectors for γ-quanta. The high pressure target filled with deuterium at temperatures from 85 K to 800 K was exposed to the negative muon beam of the JINR phasotron to detect γ-quanta with energy 23.8 MeV. The first experimental estimation for the yield of the radiative deuteron capture from the ddµ state J=1 was obtained at the level n γ ≤ 2 × 10 −5 per one fusion.