This paper explores the feasibility of power analysis attacks against low-latency block ciphers implemented with unrolled architectures capable of encryption/decryption in a single clock cycle. Unrolled architectures have been expected to be somewhat resistant against side-channel attacks compared to typical loop architectures because of no memory (i.e. register) element storing intermediate results in a synchronous manner. In this paper, we present a systematic method for selecting Points-of-Interest for power analysis on unrolled architectures as well as calculating dynamic power consumption at a target function. Then, we apply the proposed method to PRINCE, which is known as one of the most efficient low-latency ciphers, and evaluate its validity with an experiment using a set of unrolled PRINCE processors implemented on an FPGA. Finally, a countermeasure against such analysis is discussed.