The multivariate skew-normal distribution is useful for modeling departures from normality in data through parameters controlling skewness. Recently, several extensions of this distribution have been proposed in the statistical literature, among which the truncated multivariate skew-normal distribution is the foremost. Truncated distributions appear frequently in various theoretical and applied statistical problems. In this article, we study several properties of the truncated multivariate skew-normal distribution. We obtain distributional results through affine transformations, marginalization, and conditioning. Furthermore, the log-concavity of the joint probability density function is established.