G349.7 $ + $ 0.2 is a young Galactic supernova remnant ( SNR ) located at the distance of 11.5 kpc and observed across the entire electromagnetic spectrum from radio to high energy ( HE ; 0.1 GeV ¡ E ¡ 100 GeV ) \gamma -rays . Radio and infrared observations indicate that the remnant is interacting with a molecular cloud . In this paper , the detection of very high energy ( VHE , E ¿ 100 GeV ) \gamma -ray emission coincident with this SNR with the High Energy Stereoscopic System ( H.E.S.S . ) is reported . This makes it one of the farthest Galactic SNR ever detected in this domain . An integral flux F ( E > 400 \mathrm { GeV } ) = ( 6.5 \pm 1.1 _ { \mathrm { stat } } \pm 1.3 _ { \mathrm { syst } } ) % \times 10 ^ { -13 } ph cm ^ { -2 } s ^ { -1 } corresponding to \sim 0.7 % of that of the Crab Nebula and to a luminosity of \sim 10 ^ { 34 } erg s ^ { -1 } above the same energy threshold , and a steep photon index \Gamma _ { VHE } = 2.8 \pm 0.27 _ { \mathrm { stat } } \pm 0.20 _ { \mathrm { syst } } are measured . The analysis of more than 5 yr of Fermi -LAT data towards this source shows a power-law like spectrum with a best-fit photon index \Gamma _ { HE } = 2.2 \pm 0.04 _ { stat } { } ^ { +0.13 } { } _ { -0.31 } { } _ { sys } . The combined \gamma -ray spectrum of G349.7 $ + $ 0.2 can be described by either a broken power-law ( BPL ) or a power-law with exponential ( or sub-exponential ) cutoff ( PLC ) . In the former case , the photon break energy is found at E _ { br, \gamma } = 55 ^ { +70 } _ { -30 } GeV , slightly higher than what is usually observed in the HE/VHE \gamma -ray emitting middle-aged SNRs known to be interacting with molecular clouds . In the latter case , the exponential ( respectively sub-exponential ) cutoff energy is measured at E _ { cut, \gamma } = 1.4 ^ { +1.6 } _ { -0.55 } ( respectively 0.35 ^ { +0.75 } _ { -0.21 } ) TeV . A pion-decay process resulting from the interaction of the accelerated protons and nuclei with the dense surrounding medium is clearly the preferred scenario to explain the \gamma -ray emission . The BPL with a spectral steepening of 0.5-1 and the PLC provide equally good fits to the data . The product of the average gas density and the total energy content of accelerated protons and nuclei amounts to n _ { H } W _ { p } \sim 5 \times 10 ^ { 51 } erg cm ^ { -3 } .