Dynamic generalized linear models may be seen as an extension to dynamic linear models, accommodating non-Gaussian responses, and to generalized linear models, formally treating serial auto-correlation inherent to responses in the exponential family, observed through time. The Bayesian inference scheme does not have analytical solution and there are several approximating approaches in the literature, many of them relying on Monte Carlo Markov Chain, with the burden of computational cost. Other approaches are designed to assure computational efficiency, but due to modeling restrictions, fail to accommodate certain structural misbehavior which is not rare in practical applications, such as time-varying seasonal patterns. The present work revisits inference methods for this class, proposing a new approach based on information geometry, focusing on the k-parametric exponential family. Among others, the proposed method accommodates multinomial responses on k=d+1 categories. The method preserves the sequential aspect of the Bayesian inferential procedure, producing real-time inference and naturally accommodates association among k predictors. Information geometry concepts such as the projection theorem and Kullback-Leibler divergence are used in the development of the method, placing it close to recent approaches of variational inference. Applications to real data are presented, demonstrating the computational efficiency of the method, as well as its flexibility to quickly accommodate new patterns and information when strategically needed, favorably comparing to alternative approaches in the literature, preserving aspects of monitoring and intervention analysis, which are common in sequential analyses.