Data as a Service (DaaS) builds on service-oriented technologies to enable fast access to data resources on the Web. However, this paradigm raises several new concerns that traditional privacy models for Web services do not handle. First, the distinction between the roles of service providers and data providers is unclear, leaving the latter helpless for specifying and verifying the enforcement of their data privacy requirements. Second, traditional models for privacy policies focus only on the service interface without taking into account privacy policies related to data resources. Third, unstructured data resources, as well as user permissions and obligations related to data that are utilized in DaaS are not taken into account. In this paper, we study data privacy as one of these concerns, which relates to the management of private information. The main contribution of this paper consists in: 1)~devising a model for making explicit privacy constraints of DaaS, and 2)~on the basis of the proposed privacy model, developing techniques that allow handling the privacy concern when querying DaaS. We validate the applicability of our proposal with some experiments.