The single-index model is known to offer a flexible way to model a variety of high-dimensional real-world phenomena. However, despite its relative implicity, this dimension reduction scheme is faced with severe complications as soon as the underlying dimension becomes larger than the number of observations (``p larger than n'' paradigm). To circumvent this difficulty, we consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesian approach. On the theoretical side, we offer a sharp oracle inequality, which is more powerful than the best known oracle inequality for other common procedures of single-index recovery. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technique and its performance is compared with that of standard procedures.