  In this letter we dynamically determine the quadrupole mass moment Q of the
magnetic white dwarf WD 0137-349 by analyzing the period of the recently
discovered brown dwarf moving around it in a close 2-hr orbit. It turns out
that a purely Newtonian model for the orbit of WD 0137-349B, assumed circular
and equatorial, is adequate, given the present-day accuracy in knowing the
orbital parameters of such a binary system. Our result is Q=(-1.4615 +/-
0.9004) 10^47 kg m^2 for i=35 deg. It is able to accommodate the 3-sigma
significant discrepancy of (1.0 +/- 0.3) 10^-8 s^-2 between the inverse square
of the phenomenologically determined orbital period and the inverse square of
the calculated Keplerian one. The impact of i, for which a range Delta i of
possible values close to 35 deg is considered, is investigated as well.
