This paper proposes a novel approach that uses meteorological information to predict the incidence of influenza in Galicia (Spain). It extends the Generalized Least Squares (GLS) methods in the multivariate framework to functional regression models with dependent errors. These kinds of models are useful when the recent history of the incidence of influenza are readily unavailable (for instance, by delays on the communication with health informants) and the prediction must be constructed by correcting the temporal dependence of the residuals and using more accessible variables. A simulation study shows that the GLS estimators render better estimations of the parameters associated with the regression model than they do with the classical models. They obtain extremely good results from the predictive point of view and are competitive with the classical time series approach for the incidence of influenza. An iterative version of the GLS estimator (called iGLS) was also proposed that can help to model complicated dependence structures. For constructing the model, the distance correlation measure was employed to select relevant information to predict influenza rate mixing multivariate and functional variables. These kinds of models are extremely useful to health managers in allocating resources in advance to manage influenza epidemics