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We investigate whether the magnetic field of an accreting neutron star may be diamagnetically screened by the accreted matter. We assume the freshly accumulated material is unmagnetized, and calculate the rate at which the intrinsic stellar magnetic flux is transported into it by Ohmic diffusion. We calculate the one-dimensional steady-state magnetic field profiles, and show that the magnetic field strength decreases as one moves up through the outer crust and ocean by roughly (Mdot/0.02 Mdot_Edd) orders of magnitude, where Mdot is the accretion rate and Mdot_Edd the Eddington accretion rate. We show that buoyancy instabilities set a limit to the strength of any buried field of roughly 10^10-10^11 G. Our results show that magnetic screening is ineffective for Mdot<0.01 Mdot_Edd, so that, no matter how the accreted material joins onto the star, the underlying stellar field should always be evident. In this respect, we point out the only known persistently-pulsing accreting X-ray millisecond pulsar, SAX J1808.4-3658, has an accretion rate of 10^-3 Mdot_Edd, far below the regime where magnetic screening can play a role. Most steadily accreting neutron stars in low-mass X-ray binaries in our Galaxy accrete at rates where screening would be effective if the simplified magnetic and accretion geometry we adopt were correct. If screened, then the underlying field will emerge after accretion halts, on a timescale of only 100--1000 years, set by the Ohmic diffusion time across the outer crust. It thus seems unlikely that screening alone can explain the low magnetic fields of the millisecond radio pulsars.