As cyber-attacks increase in unencrypted communication environments such as the traditional Internet, protected communication channels based on cryptographic protocols, such as transport layer security (TLS), have been introduced to the Internet. Accordingly, attackers have been carrying out cyber-attacks by hiding themselves in protected communication channels. However, the nature of channels protected by cryptographic protocols makes it difficult to distinguish between normal and malicious network traffic behaviors. This means that traditional anomaly detection models with features from packets extracted a deep packet inspection (DPI) have been neutralized. Recently, studies on anomaly detection using artificial intelligence (AI) and statistical characteristics of traffic have been proposed as an alternative. In this review, we provide a systematic review for AI-based anomaly detection techniques over encrypted traffic. We set several research questions on the review topic and collected research according to eligibility criteria. Through the screening process and quality assessment, 30 research articles were selected with high suitability to be included in the review from the collected literature. We reviewed the selected research in terms of dataset, feature extraction, feature selection, preprocessing, anomaly detection algorithm, and performance indicators. As a result of the literature review, it was confirmed that various techniques used for AI-based anomaly detection over encrypted traffic were used. Some techniques are similar to those used for AI-based anomaly detection over unencrypted traffic, but some technologies are different from those used for unencrypted traffic.