  We study the surface tension of highly magnetized three flavor quark matter
within the formalism of multiple reflection expansion (MRE). Quark matter is
described as a mixture of free Fermi gases composed by quarks $u$, $d$, $s$ and
electrons, in chemical equilibrium under weak interactions. Due to the presence
of strong magnetic fields the particles' transverse motion is quantized into
Landau levels, and the surface tension has a different value in the parallel
and transverse directions with respect to the magnetic field.
  We calculate the transverse and longitudinal surface tension for different
values of the magnetic field and for quark matter drops with different sizes,
from a few fm to the bulk limit. For baryon number densities between $2-10$
times the nuclear saturation density, the surface tension falls in the range $2
- 20$ MeV /fm$^{2}$. The largest contribution comes from strange quarks which
have a surface tension an order of magnitude larger than the one for $u$ or $d$
quarks and more than two orders of magnitude larger than for electrons. Our
results show that the total surface tension is quite insensitive to the size of
the drop. We also find that the surface tensions in the transverse and parallel
directions are almost unaffected by the magnetic field if $eB$ is below $\sim 5
\times 10^{-3} $ GeV$^2$. Nevertheless, for higher values of $eB$, there is a
significant increase in the parallel surface tension and a significant decrease
in the transverse one with respect to the unmagnetized case.
