[en] The german-british neutrino experiment Karmen is performed at the spallation neutron source ISIS (Chilton, UK). The principal aims beside the search of neutrino flavour oscillations are the investigations of neutrino-nucleus interactions. The two-body decay of π⁺ in rest generates monoenergetic muon neutrinos with energy E=29.8 MeV. The present work describes the first observation of the weak neutral current reaction ¹²C(ν_μ,ν^'_μ)¹²C^*(1⁺1; 15.1 MeV) induced by monoenergetic muon neutrinos. The unique time structure allows an independent analysis of the weak neutral current ¹²C(ν,ν^')¹²C^* by ν_μ. The cross section is determined to σ=[2.75±0.67(stat.)±0.40(sys.)] x 10^-42 cm^-2. The excited ¹²C-level acts like a spin-isospin filter and so from the cross section the isovectoriell-axial coupling constant β can be calculated to β=1.04±0.15. (orig.)