This paper is devoted to a statistical physiological functional variable selection for driver's stress level classification using random forests. Indeed, this study focuses on humans physiological changes, produced when driving in different urban routes, captured using portable sensors. Specifically, the electrodermal activity measured on two different locations: hand and foot, electromyogram, heart rate and respiration of ten driving experiments in three types of routes: rest area, city, and highway driving issued from drivedb database, available online on the PhysioNet website. Several studies were achieved on driver's stress level recognition using physiological signals. Classically, researchers extract expert-based features from physiological signals and select the most relevant ones for stress level recognition. This work provides a random forest-based method for the selection of physiological functional variables in order to classify the driver's stress level. On the methodological side, the contributions of this work are to consider physiological signals as functional variables, decomposed on wavelet basis and to offer a procedure of variable selection. On the applied side, the proposed method provides a " blind " procedure of driver's stress level classification performing as the expert-based study in terms of misclassification rate. It offers moreover a ranking of physiological variables according to their importance in stress level classification. The obtained results suggest that electromyogram and heart rate signals are not very relevant when compared to the electro-dermal and the respiration signals.