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 (omega(X)Xi(X) + 2 pi phi(X)), one linearly spaced in k space with Xi(lin) equivalent to k/k(*) where k(*) = 0.05 Mpc(-1) and the other logarithmically spaced in k space with Xi(log) equivalent to ln(k/k(*)). We note that AX is the amplitude of the primordial feature, omega(X) is the dimensionless frequency, and phi(X) is the normalised phase, where X = {lin, log}. We provide forecasts from spectroscopic and photometric primary Euclid probes on the standard cosmological parameters Omega(m,0), Omega(b,0), h, ns, and sigma(8), and the primordial feature parameters A(X), omega(X), and phi(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 di fferent 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, omega(X) = 10, and phi(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) similar or equal to 0.010 +/- 0.001 at a 68.3% CL and A(log) similar or equal to 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)).