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 } = 7.14846 d ^ { -1 } ) and by rotational modulation ( P _ { rot } = 3.638833 d ) . Two non-radial low-amplitude modes ( f _ { 2 } = 7.75603 d ^ { -1 } and f _ { 3 } = 6.82308 d ^ { -1 } ) are also detected . The four periodicities that we found are the same as the ones discovered from a companion multisite photometric campaign ( Handler et al . ( 39 ) ) and known in the literature . Using the photometric constraints on the degrees \ell of the pulsation modes , we show that both f _ { 2 } and f _ { 3 } are prograde modes with ( \ell,m ) = ( 4 , 2 ) or ( 4 , 3 ) . These results allowed us to deduce ranges for the mass ( M \in [ 8.2 , 9.6 ] M _ { \odot } ) and central hydrogen abundance ( X _ { c } \in [ 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 } \in [ 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 } \in [ 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 .