Data from the Sudbury Neutrino Observatory have been used to constrain the lifetime for nucleon decay to "invisible" modes, such as n-->3nu. The analysis was based on a search for gamma rays from the deexcitation of the residual nucleus that would result from the disappearance of either a proton or neutron from 16O. A limit of tau(inv)>2 x 10(29) yr is obtained at 90% confidence for either neutron- or proton-decay modes. This is about an order of magnitude more stringent than previous constraints on invisible proton-decay modes and 400 times more stringent than similar neutron modes.