The Euclid Early Release Observations (ERO) programme targeted the Perseus cluster of galaxies, gathering deep data in the central region of the cluster over 0.7 deg2, including the cluster core up to 0.25 r200. The dataset reaches a point-source depth of IE = 28.0 (YE, JE, HE = 25.3), AB magnitudes at 5 σ with a 0′′ . 16 (0′′ . 48) full width at half maximum (FWHM), and a surface brightness limit of 30.1 (29.2) mag arcsec−2 for radially integrated galaxy profiles. The exceptional depth and spatial resolution of this wide-field multi-band data enable simultaneous detection and characterisation of both bright galaxies and low surface brightness ones, along with their globular cluster systems, from the optical to the near-infrared (NIR). Cluster membership was determined using several methods in order to maximise the completeness and minimise the contamination of foreground and background sources. We adopted a catalogue of 1100 dwarf galaxies, detailed in the corresponding ERO paper, that includes their photometric and structural properties. We identified all other sources in the Euclid images and obtained accurate photometric measurements using AutoProf or AstroPhot for 137 bright cluster galaxies and SourceExtractor for half a million compact sources. This study advances beyond previous analyses of the cluster and enables a range of scientific investigations, which are summarised here. We derived the luminosity and stellar mass functions (LF and SMF) of the Perseus cluster in the Euclid IE band thanks to supplementary u, g, r, i, z, and Hα data from the Canada-France-Hawai’i Telescope (CFHT). Our LF and SMF are the deepest recorded for the Perseus cluster, highlighting the groundbreaking capabilities of the Euclid telescope. We fit the LF and SMF with a Schechter plus Gaussian model. The LF features a dip at M(IE) ≃ −19 and a faint-end slope of αS ≃ −1.2 to −1.3. The SMF displays a low-mass-end slope of αS ≃ −1.2 to −1.35. These observed slopes are flatter than those predicted for dark matter halos in cosmological simulations, offering significant insights for models of galaxy formation and evolution.