Early event detection aims to detect events even before the event is complete. However, most of the existing methods focus on an event with a single label but fail to be applied to cases with multiple labels. Another non-negligible issue for early event detection is a prediction with overconfidence due to the high vacuity uncertainty that exists in the early time series. It results in an over-confidence estimation and hence unreliable predictions. To this end, technically, we propose a novel framework, Multi-Label Temporal Evidential Neural Network (MTENN), for multi-label uncertainty estimation in temporal data. MTENN is able to quality predictive uncertainty due to the lack of evidence for multi-label classifications at each time stamp based on belief/evidence theory. In addition, we introduce a novel uncertainty estimation head (weighted binomial comultiplication (WBC)) to quantify the fused uncertainty of a sub-sequence for early event detection. We validate the performance of our approach with state-of-the-art techniques on real-world audio datasets.