Primordial features, in particular oscillatory signals, imprinted in the primordial power spectrum of density perturbations represent a clear window of opportunity for detecting new physics at high-energy scales. Future spectroscopic and photometric measurements from the Euclid space mission will provide unique constraints on the primordial power spectrum, thanks to the redshift coverage and high-accuracy measurement of nonlinear scales, thus allowing us to investigate deviations from the standard power-law primordial power spectrum. We consider two models with primordial undamped oscillations superimposed on the matter power spectrum described by 1 + 𝒜_X sin (ω_XΞ_X + 2 πϕ_X), one linearly spaced in k space with Ξ_lin ≡ k/k_* where k_* = 0.05 Mpc⁻¹ and the other logarithmically spaced in k space with Ξ_log ≡ ln(k/k_*). We note that 𝒜_X is the amplitude of the primordial feature, ω_X is the dimensionless frequency, and ϕ_X is the normalised phase, where X = {lin, log}. We provide forecasts from spectroscopic and photometric primary Euclid probes on the standard cosmological parameters Ω_{m, 0}, Ω_{b, 0}, h, n_s, and σ₈, and the primordial feature parameters 𝒜_X, ω_X, and ϕ_X. We focus on the uncertainties of the primordial feature amplitude 𝒜_X and on the capability of Euclid to detect primordial features at a given frequency. We also study a nonlinear density reconstruction method in order to retrieve the oscillatory signals in the primordial power spectrum, which are damped on small scales in the late-time Universe due to cosmic structure formation. Finally, we also include the expected measurements from Euclid’s galaxy-clustering bispectrum and from observations of the cosmic microwave background (CMB). We forecast uncertainties in estimated values of the cosmological parameters with a Fisher matrix method applied to spectroscopic galaxy clustering (GC_sp), weak lensing (WL), photometric galaxy clustering (GC_ph), the cross correlation (XC) between GC_ph and WL, the spectroscopic galaxy clustering bispectrum, the CMB temperature and E-mode polarisation, the temperature-polarisation cross correlation, and CMB weak lensing. We consider two sets of specifications for the Euclid probes (pessimistic and optimistic) and three different CMB experiment configurations, that is, Planck, Simons Observatory (SO), and CMB Stage-4 (CMB-S4). We find the following percentage relative errors in the feature amplitude with Euclid primary probes: for the linear (logarithmic) feature model, with a fiducial value of 𝒜_X = 0.01, ω_X = 10, and ϕ_X = 0: 21% (22%) in the pessimistic settings and 18% (18%) in the optimistic settings at a 68.3% confidence level (CL) using GC_sp+WL+GC_ph+XC. While the uncertainties on the feature amplitude are strongly dependent on the frequency value when single Euclid probes are considered, we find robust constraints on 𝒜_X from the combination of spectroscopic and photometric measurements over the frequency range of (1, 10^2.1). Due to the inclusion of numerical reconstruction, the GC_sp bispectrum, SO-like CMB reduces the uncertainty on the primordial feature amplitude by 32%–48%, 50%–65%, and 15%–50%, respectively. Combining all the sources of information explored expected from Euclid in combination with the future SO-like CMB experiment, we forecast 𝒜_lin ≃ 0.010 ± 0.001 at a 68.3% CL and 𝒜_log ≃ 0.010 ± 0.001 for GC_sp(PS rec + BS)+WL+GC_ph+XC+SO-like for both the optimistic and pessimistic settings over the frequency range (1, 10^2.1).