We study the consequences of invisible decay of neutrinos in the context of the DUNE experiment. We assume that the third mass eigenstate is unstable and decays to a light sterile neutrino and a scalar or a pseudo-scalar. We consider DUNE running in 5 years neutrino and 5 years antineutrino mode and a detector volume of 40 kt. We obtain the expected sensitivity on the rest-frame life-time tau(3) normalized to the mass m(3) as tau(3)/m(3) > 4.50 x 10(-11) s/eV at 90% C.L. for a normal hierarchical mass spectrum. We also find that DUNE can discover neutrino decay for tau(3)/m(3) > 4.27 x 10(-11) s/eV at 90% C.L. In addition, for an unstable tau(3) with an illustrative value of tau(3)/m(3) = 1.2 x 10(-11) s/eV, the no decay case could get disfavoured at the 3 sigma C.L. At 90% C.L. the expected precision range for this true value is obtained as 1.71 x 10(-11 >) tau(3)/m(3) > 9.29 x 10(-12) in units of s/eV. We also study the correlation between a non-zero tau(3)/m(3) and standard oscillation parameters and find an interesting correlation in the appearance and disappearance channels with the mixing angle theta(23). This alters the octant sensitivity of DUNE, favorably (unfavorably) for true theta(23) in the lower (higher) octant. The effect of a decaying neutrino does not alter the hierarchy or CP violation discovery sensitivity of DUNE in a discernible way.