  In this paper we extend the well known QCD sum rules used in the calculation
of the mass of heavy mesons to estimate the modification of the charged B meson
mass, m_B, in the presence of an external Abelian magnetic field, eB. Two
simplifying limits were considered: the weak field limit in which the external
field satisfies eB << m^2 (with m being any of the masses involved) and the
strong field limit in which the field strength is small in comparison to the
bottom quark mass (or the B meson mass) squared but it is large compared to the
mass of the light quarks, i.e., m^2_{u,d} << eB << m^2_{b,B}. We found that m_B
decreases with the magnetic field in the both of these limits.
