Predicting dynamics of host-microbial ecosystems is crucial for rational design of bacteriotherapies. We present MDSINE, a suite of algorithms for inferring dynamical systems models from microbiome time-series data and predicting temporal behaviors. Using simulated data, we demonstrate that MDSINE significantly outperforms the existing inference method. We then demonstrate MDSINE’s utility on two new gnotobiotic mice datasets, investigating infection with Clostridium difficile and an immune-modulatory probiotic. On these datasets, we demonstrate new capabilities including accurate forecasting of microbial dynamics, prediction of stable sub-communities that inhibit pathogen growth, and identification of bacteria most crucial to community integrity (keystoneness) in response to perturbations.