Mental stress is on the rise as one of the major health problems in modern society. It is important to detect and manage mental stress to prevent various diseases caused by stress and to maintain a healthy life. The purpose of this paper is to present new heart rate variability (HRV) features based on empirical mode decomposition and to detect acute mental stress through short-term HRV (5 min) and ultra-short-term HRV (under 5 min) analysis. HRV signals were acquired from 74 young police officers using acute stressors, including the Trier Social Stress Test and horror movie viewing, and a total of 26 features, including the proposed IMF energy features and general HRV features, were extracted. A support vector machine (SVM) classification model is used to classify the stress and non-stress states through leave-one-subject-out cross-validation. The classification accuracies of short-term HRV and ultra-short-term HRV analysis are 86.5% and 90.5%, respectively. In the results of ultra-short-term HRV analysis using various time lengths, we suggest the optimal duration to detect mental stress, which can be applied to wearable devices or healthcare systems.