We present EMVSNet, a sampling-free Multi-View Stereo (MVS) method that, to the best of our knowledge, is the first to integrate Evidential Deep Learning into MVS. Given a set of overlapping images, our method predicts a depth value together with its associated uncertainty per pixel of a reference image, incorporating uncertainty from aleatoric and epistemic sources. Specifically, we use an existing convolutional neural network architecture designed for MVS as backbone and extend it to regress evidential parameters per pixel, describing the probability distribution over the depth corresponding to this pixel. In contrast to existing MVS methods that often neglect epistemic uncertainty or obtain it via sampling at inference, our evidential formulation does not require sampling, but enables single-pass inference. We evaluate the uncertainty estimation capabilities of our method using two publicly available datasets and compare the depth predictions against a deterministic variant. The experimental results demonstrate that EMVSNet achieves competitive depth accuracy while, at the same time, providing uncertainty estimates that enable us to reliably rank depth estimates according to their risk of being incorrect and to automatically identify out of distribution data. Our model shows only slightly increased inference time compared to a deterministic baseline while giving comparable uncertainty estimates to an computationally expensive sampling based approach, marking a first step towards real-time capable uncertainty estimation for image-based 3D reconstruction. Our code is available at: <code>https://github.com/BuTTerK3ks/EMVSNet</code>.