This paper addresses consensus-based networked estimation of the state of a nonlinear dynamical system. This paper first presents an information form of the recently proposed Bayesian recursive update filter (BRUF), a Kalman filter that uses a recursive update to incorporate information from nonlinear measurement systems. Under the assumptions that the system is collectively observable and the network is strongly connected, a distributed information Bayesian recursive update filter (DIBRUF), a distributed form of the information Bayesian recursive update filter (IBRUF), is proposed, which exploits consensus on information vectors and matrices. Compared to the distributed extended Kalman filter (DEKF), the DIBRUF reduces the linearization error of the extended Kalman filter (EKF) by dividing the measurement update into N steps. Unlike the BRUF and IBRUF, which require local observability, the DIBRUF requires only the network to be collectively observable, as the sensors can share information among the network. Simulation experiments demonstrate the validity of the proposed approach.