We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk [5]. We recapture and make use of the convenient calculus on Frechet spaces, as developed by Kriegl and Michor [16]. Our main result is a weak version of the Frobenius theorem on Frechet spaces. As an application we characterize all finite-dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates