We used extensive ground-based multisite and archival spectroscopy to derive observational constraints for a seismic modelling of the magnetic β Cep star V2052 Ophiuchi. The line-profile variability is dominated by a radial mode (f1 = 7.148 46 d−1) and by rotational modulation (Prot = 3.638 833 d). Two non-radial low-amplitude modes (f2 = 7.756 03 d−1 and f3 = 6.823 08 d−1) are also detected. The four periodicities that we found are the same as the ones discovered from a companion multisite photometric campaign and known in the literature. Using the photometric constraints on the degrees ℓ of the pulsation modes, we show that both f2 and f3 are prograde modes with (ℓ, m) = (4, 2) or (4, 3). These results allowed us to deduce ranges for the mass (M ∈ [8.2, 9.6] M⊙) and central hydrogen abundance (Xc ∈ [0.25, 0.32]) of V2052 Oph, to identify the radial orders n1 = 1, n2 = −3 and n3 = −2, and to derive an equatorial rotation velocity veq ∈ [71, 75] km s−1. The model parameters are in full agreement with the effective temperature and surface gravity deduced from spectroscopy. Only models with no or mild core overshooting (αov ∈ [0, 0.15] local pressure scale heights) can account for the observed properties. Such a low overshooting is opposite to our previous modelling results for the non-magnetic β Cep star θ Oph having very similar parameters, except for a slower surface rotation rate. We discuss whether this result can be explained by the presence of a magnetic field in V2052 Oph that inhibits mixing in its interior.