Approximation-aware testing has been recently proposed because conventional methods cannot take into account the flexibility encountered in approximate circuits for handling errors. However, the security vulnerabilities of approximation-aware testing techniques have not been fully considered. Approximate circuits utilize several schemes with a variety of error patterns, that open new opportunities for attackers. In this paper, the security threats in approximation-aware testing methods are investigated. To the best of the authors' knowledge, the topic on the security analysis of approximation-aware testing techniques has not been treated in the technical literature. Two malicious tampering attacks are proposed in addition to an attack that can invalidate hardware Trojan detection. The proposed two tampering attacks, namely tampering of the exact netlist (TEN) and tampering of the error metric (TEM), are evaluated with experiments. The results show that original non-acceptable faults can be mistakenly assigned as acceptable faults and that approximation-aware testing techniques can invalidate the detection of hardware Trojans in approximate circuits due to fault classification.