Besides the opportunities offered by the all-embracing Internet of Things (IoT) technology, it also poses a tremendous threat to the privacy of the carriers of these devices. In this work, we build upon the idea of an RFID-based IoT realized by means of standardized and well-established Internet protocols. In particular, we demonstrate how the Internet Protocol Security protocol suite (IPsec) can be applied in a privacy-aware manner. Therefore, we introduce a privacy-aware mutual authentication protocol compatible with restrictions imposed by the IPsec standard and analyze its privacy and security properties. In order do so, we revisit and adapt the RFID privacy model (HPVP) of Hermans et al. (ESORICS’11). With this work, we show that privacy in the IoT can be achieved without relying on proprietary protocols and on the basis of existing Internet standards.