This paper proposes a privacy-preserving data fusion method for traffic state estimation (TSE). Unlike existing works that assume all data sources to be accessible by a single trusted party, we explicitly address data privacy concerns that arise in the collaboration and data sharing between multiple data owners, such as municipal authorities (MAs) and mobility providers (MPs). To this end, we propose a novel vertical federated learning (FL) approach, FedTSE, that enables multiple data owners to collaboratively train and apply a TSE model without having to exchange their private data. To enhance the applicability of the proposed FedTSE in common TSE scenarios with limited availability of ground-truth data, we further propose a privacy-preserving physics-informed FL approach, i.e., FedTSE-PI, that integrates traffic models into FL. Real-world data validation shows that the proposed methods can protect privacy while yielding similar accuracy to the oracle method without privacy considerations.