Quality Estimation (QE) is the task of predicting the quality of Machine Translation (MT) system output, without using any gold-standard translation references. State-of-the-art QE models are supervised: they require human-labeled quality of some MT system output on some datasets for training, making them domain-dependent and MT-system-dependent. There has been research on unsupervised QE, which requires glass-box access to the MT systems, or parallel MT data to generate synthetic errors for training QE models. In this paper, we present Perturbation-based QE - a word-level Quality Estimation approach that works simply by analyzing MT system output on perturbed input source sentences. Our approach is unsupervised, explainable, and can evaluate any type of blackbox MT systems, including the currently prominent large language models (LLMs) with opaque internal processes. For language directions with no labeled QE data, our approach has similar or better performance than the zero-shot supervised approach on the WMT21 shared task. Our approach is better at detecting gender bias and word-sense-disambiguation errors in translation than supervised QE, indicating its robustness to out-of-domain usage. The performance gap is larger when detecting errors on a nontraditional translation-prompting LLM, indicating that our approach is more generalizable to different MT systems. We give examples demonstrating our approach's explainability power, where it shows which input source words have influence on a certain MT output word.