We report the discovery of a complete Einstein ring around the elliptical galaxy NGC 6505, at z = 0.042. This is the first strong gravitational lens discovered in Euclid and the first in an NGC object from any survey. The combination of the low redshift of the lens galaxy, the brightness of the source galaxy (IE = 18.1 lensed, IE = 21.3 unlensed), and the completeness of the ring make this an exceptionally rare strong lens, unidentified until its observation by Euclid. We present deep imaging data of the lens from the Euclid Visible Camera (VIS) and Near-Infrared Spectrometer and Photometer (NISP) instruments, as well as resolved spectroscopy from the Keck Cosmic Web Imager (KCWI). The Euclid imaging in particular presents one of the highest signal-to-noise ratio optical/near-infrared observations of a strong gravitational lens to date. From the KCWI data we measure a source redshift of z = 0.406. Using data from the Dark Energy Spectroscopic Instrument (DESI) we measure a velocity dispersion for the lens galaxy of σ∗ = 303 ± 15 km s-1. We model the lens galaxy light in detail, revealing angular structure that varies inside the Einstein ring. After subtracting this light model from the VIS observation, we model the strongly lensed images, finding an Einstein radius of 2.″5, corresponding to 2.1 kpc at the redshift of the lens. This is small compared to the effective radius of the galaxy, Reff ∼ 12.″3. Combining the strong lensing measurements with analysis of the spectroscopic data we estimate a dark matter fraction inside the Einstein radius of fDM = (11.1-3.5+5.4)% and a stellar initial mass-function (IMF) mismatch parameter of αIMF = 1.26-0.08+0.05, indicating a heavier-than-Chabrier IMF in the centre of the galaxy.