Although sample size calculations for testing a parameter in the Poisson regression model have been previously done, very little attention has been given to the effect of the correlation structure of the covariates on the sample size except for the work of Shieh (2001) where several different values of the parameters of the multinomial distribution were considered. We propose to calculate the sample size for the Wald test in the Poisson regression model, assuming that the covariates may be correlated and have a multivariate normal distribution. We have chosen the two most popular correlation structures, that is, the exchangeable and the AR(1) correlation matrices, with different values for the correlation to illustrate our work. The method used here to calculate the sample size is based on a modification of the methodology proposed by Shieh (2001). Using Monte Carlo simulations, we conclude that the sample size depends on the number of covariates for the exchangeable correlation matrix, but much more so on the correlation structure. The AR(1) correlation matrix does not exhibit these types of changes. Our methodology is also extended for the case of the Zero-inflated Poisson regression model in order to obtain analogous results there.