The intracluster light (ICL) permeating galaxy clusters is a tracer of the cluster assembly history and potentially a tracer of their dark matter structure. In this work, we explore the capability of the Euclid Wide Survey to detect ICL using HE-band mock images. We simulated clusters across a range of redshifts (0.3–1.8) and halo masses (1013.9–1015.0 M⊙) using an observationally motivated model of ICL. We identified a 50–200 kpc circular annulus around the brightest cluster galaxy (BCG) in which the signal-to-noise ratio of the ICL is maximised and used the S/N within this aperture as our figure of merit for ICL detection. We compared three state-of-the-art methods for ICL detection and found that a method that performs simple aperture photometry after high-surface brightness source masking is able to detect ICL with minimal bias for clusters more massive than 1014.2 M⊙. The S/N of the ICL detection is primarily limited by the redshift of the cluster, which is driven by cosmological dimming rather than the mass of the cluster. Assuming the ICL in each cluster contains 15% of the stellar light, we forecast that Euclid will be able to measure the presence of ICL in up to ∼80 000 clusters of >1014.2 M⊙ between z = 0.3 and 1.5 with an S/N>3. Half of these clusters will reside below z = 0.75, and the majority of those below z = 0.6 will be detected with an S/N>20. A few thousand clusters at 1.3<z<1.5 will have ICL detectable with an S/N >3. The surface brightness profile of the ICL model is strongly dependent on both the mass of the cluster and the redshift at which it is observed so that the outer ICL is best observed in the most massive clusters of >1014.7 M⊙. Euclid will detect the ICL at a distance of more than 500 kpc from the BCG, up to z = 0.7, in several hundred of these massive clusters over its large survey volume.