  Based on the model of the accretion-induced magnetic field decay of a neutron
star (NS), millisecond pulsars (MSPs) will obtain their minimum magnetic field
when the NS magnetosphere radius shrinks to the stellar surface during the
binary accretion phase. We find that this minimummagnetic field is related to
the accretion rate Mdot as Bmin ~2.0*10^7 G( Mdot/Mdot_min)^1/2, where Mdot_min
= 4.6*10^15 g/s is the average minimum accretion rate required for MSP
formation and is constrained by the long-term accretion time, which corresponds
to the companion lifetime, being less than the Hubble time. The value of Bmin
is consistent with that of observed radio MSPs and accreting MSPs in low-mass
X-ray binaries, which can be found the illustrated case of the minimum and
present field strength of SAX J1808.4-3658. The prediction of the minimum
magnetic field of MSPs would be the lowest field strength of NSs in the
Universe, which could constrain the evolution mechanism of the magnetic field
of accreting NSs.
