In order to improve mobile data transparency, a number of network-based approaches have been proposed to inspect packets generated by mobile devices and detect personally identifiable information (PII), ad requests, or other activities. State-of-the-art approaches train classifiers based on features extracted from HTTP packets. So far, these classifiers have only been trained in a centralized way, where mobile users label and upload their packet logs to a central server, which then trains a global classifier and shares it with the users to apply on their devices. However, packet logs used as training data may contain sensitive information that users may not want to share/upload. In this paper, we apply, for the first time, a Federated Learning approach to mobile packet classification, which allows mobile devices to collaborate and train a global model, without sharing raw training data. Methodological challenges we address in this context include: model and feature selection, and tuning the Federated Learning parameters. We apply our framework to two different packet classification tasks (i.e., to predict PII exposure or ad requests in HTTP packets) and we demonstrate its effectiveness in terms of classification performance, communication and computation cost, using three real-world datasets.