Context. As part of our international program aimed at obtaining accurate physical properties of trans-Neptunian objects (TNOs), we predicted a stellar occultation by the TNO (38628) Huya of the star Gaia DR2 4352760586390566400 (m_G = 11.5 mag) on March 18, 2019. After an extensive observational campaign geared at obtaining the astrometric data, we updated the prediction and found it favorable to central Europe. Therefore, we mobilized half a hundred of professional and amateur astronomers in this region and the occultation was finally detected by 21 telescopes located at 18 sites in Europe and Asia. This places the Huya event among the best ever observed stellar occultation by a TNO in terms of the number of chords. Aims. The aim of our work is to determine an accurate size, shape, and geometric albedo for the TNO (38628) Huya by using the observations obtained from a multi-chord stellar occultation. We also aim to provide constraints on the density and other internal properties of this TNO. Methods. The 21 positive detections of the occultation by Huya allowed us to obtain well-separated chords which permitted us to fit an ellipse for the limb of the body at the moment of the occultation (i.e., the instantaneous limb) with kilometric accuracy. Results. The projected semi-major and minor axes of the best ellipse fit obtained using the occultation data are (a⁰, b⁰) = (217.6 ± 3.5 km, 194.1 ± 6.1 km) with a position angle for the minor axis of P⁰ = 55.2^◦ ± 9.1. From this fit, the projected area-equivalent diameter is 411.0 ± 7.3 km. This diameter is compatible with the equivalent diameter for Huya obtained from radiometric techniques (D = 406 ± 16 km). From this instantaneous limb, we obtained the geometric albedo for Huya (p_V = 0.079 ± 0.004) and we explored possible three-dimensional shapes and constraints to the mass density for this TNO. We did not detect the satellite of Huya through this occultation, but the presence of rings or debris around Huya was constrained using the occultation data. We also derived an upper limit for a putative Pluto-like global atmosphere of about p_surf = 10 nbar.