  The Bose-Einstein condensate/scalar field dark matter model, considers that
the dark matter is composed by spinless-ultra-light particles which can be
described by a scalar field. This model is an alternative model to the
$\Lambda$-cold dark matter paradigm, and therefore should be studied at
galactic and cosmological scales. Dwarf spheroidal galaxies have been very
useful when studying any dark matter theory, because the dark matter dominates
their dynamics. In this paper we study the Sextans dwarf spheroidal galaxy,
embedded in a scalar field dark matter halo. We explore how the dissolution
time-scale of the stellar substructures in Sextans, constrain the mass, and the
self-interacting parameter of the scalar field dark matter boson. We find that
for masses in the range $(0.12< m_{\phi}<8) \times10^{-22}$~eV, scalar field
dark halos without self-interaction would have cores large enough to explain
the longevity of the stellar substructures in Sextans, and small enough mass to
be compatible with dynamical limits. If the self-interacting parameter is
distinct to zero, then the mass of the boson could be as high as
$m_{\phi}\approx2\times10^{-21}$~eV, but it would correspond to an unrealistic
low mass fot the Sextans dark matter halo . Therefore, the Sextans dwarf galaxy
could be embedded in a scalar field/BEC dark matter halo with a preferred
self-interacting parameter equal to zero.
