  We investigate a trapped surface and naked singularity in a $D$-dimensional
Vaidya spacetime with a self-similar mass function. A trapped surface is
defined as a closed spacelike $(D-2)$-surface which has negative both null
expansions. There is no trapped surface in the Minkowski spacetime. However, in
a four-dimensional self-similar Vaidya spacetime, Bengtsson and Senovilla
considered non-spherical trapped surfaces and showed that a trapped surface can
penetrate into a flat region, if and only if the mass function rises fast
enough [I. Bengtsson and J. M. M. Senovilla, Phys. Rev. D \textbf{79}, 024027
(2009).]. We apply this result to a $D$-dimensional spacetime motivated by the
context of large extra dimensions or TeV-scale gravity. In this paper,
similarly to Bengtsson and Senovilla's study, we match four types of
$(D-2)$-surfaces and show that a trapped surface extended into the flat region
can be constructed in the $D$-dimensional Vaidya spacetime, if the increasing
rate of the mass function is greater than 0.4628. Moreover, we show that the
maximum radius of the trapped surface constructed here approaches the
Schwarzschild-Tangherlini radius in the large $D$ limit. Also, we show that
there is no naked singularity, if the spacetime has the trapped surface
constructed here.
