The segment of post-quantum cryptography rises its importance with increasing improvements in the quantum computing. Cryptographic post-quantum algorithms have been proposed since 1970s. However, side-channel attack vulnerabili-ties of these algorithms are still in focus of the recent research. In this paper, we present a differential power analysis attack on the McEliece public-key cryptosystem. We demonstrate that a part of a private key, permutation matrix, can be recovered using the power analysis. We attack a software implementation of a secure bit permutation that was proposed by Strenzke et al. at PQCrypto 2008. The cryptosystem is implemented on a 32-bit ARM based microcontroller. We provide details of the attack and results using power consumption measurements of the device. In addition, we outline a novel countermeasure against the introduced attack. The countermeasure uses properties of the linear codes and does not require large amount of random bits which can be profitable for low-cost embedded devices.