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The ESA Euclid mission will provide high-quality imaging for about 1.5billion galaxies. A software pipeline to automatically process and analyse sucha huge amount of data in real time is being developed by the Science GroundSegment of the Euclid Consortium; this pipeline will include a model-fittingalgorithm, which will provide photometric and morphological estimates ofparamount importance for the core science goals of the mission and for legacyscience. The Euclid Morphology Challenge is a comparative investigation of theperformance of five model-fitting software packages on simulated Euclid data,aimed at providing the baseline to identify the best suited algorithm to beimplemented in the pipeline. In this paper we describe the simulated data set,and we discuss the photometry results. A companion paper (Euclid Collaboration:Bretonni\`ere et al. 2022) is focused on the structural and morphologicalestimates. We created mock Euclid images simulating five fields of view of 0.48deg2 each in the $I_E$ band of the VIS instrument, each with three realisationsof galaxy profiles (single and double S\'ersic, and 'realistic' profilesobtained with a neural network); for one of the fields in the double S\'ersicrealisation, we also simulated images for the three near-infrared $Y_E$, $J_E$and $H_E$ bands of the NISP-P instrument, and five Rubin/LSST opticalcomplementary bands ($u$, $g$, $r$, $i$, and $z$). To analyse the results wecreated diagnostic plots and defined ad-hoc metrics. Five model-fittingsoftware packages (DeepLeGATo, Galapagos-2, Morfometryka, ProFit, andSourceXtractor++) were compared, all typically providing good results. (cut)

Euclid preparation. XXV. The Euclid Morphology Challenge -- Towards model-fitting photometry for billions of galaxies