This article is concerned with the problem of event-based remote state estimation for nonlinear/non-Gaussian systems on a wireless network with limited bandwidth. To reduce unnecessary data transmissions, a novel event-triggering mechanism is developed by using the least-square technique. Based on this, an event-triggered box particle filtering scheme is designed to realize the minimum mean-squared error estimation at the remote estimator end, in which the posterior probability density functions are calculated separately according to the information of the event-triggered indicator to avoid the problem of excessive estimation error. Different from the existing approaches, the proposed algorithm does not depend on any Gaussian assumptions and reduces the computational complexity under the premise of ensuring the estimation performance. Finally, two simulation examples are performed to demonstrate the validity of the proposed algorithm.