Let A be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semihomogeneous vector bundles on A from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For H=0 our moduli space may be identified with the moduli space M0,r(A)
Nearby in the stack
of semistable vector bundles with vanishing Chern classes on
A
. In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of
A
onto
M0,r(A)
, which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of