We used extensive ground-based multisite and archival spectroscopy to derive observational constraints for a seismic modelling of the magnetic beta Cep star V2052 Ophiuchi. The line-profile variability is dominated by a radial mode (f(1) = 7.148 46 d(-1)) and by rotational modulation (P-rot = 3.638 833 d). Two non-radial low-amplitude modes (f(2) = 7.756 03 d(-1) and f(3) = 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 f(2) and f(3) are prograde modes with (l, m) = (4, 2) or (4, 3). These results allowed us to deduce ranges for the mass (M is an element of [8.2, 9.6] M-circle dot) and central hydrogen abundance (X-c is an element of [0.25, 0.32]) of V2052 Oph, to identify the radial orders n(1) = 1, n(2) = -3 and n(3) = -2, and to derive an equatorial rotation velocity v(eq) is an element of [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 (alpha(ov) is an element of [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 beta Cep star theta 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.