The accurate prediction of protein druggability (propensity to bind high-affinity drug-like small molecules) would greatly benefit the fields of chemical genomics and drug discovery. We have developed a novel approach to quantitatively assess protein druggability by computationally screening a fragment-like compound library. In analogy to NMR-based fragment screening, we dock approximately 11,000 fragments against a given binding site and compute a computational hit rate based on the fraction of molecules that exceed an empirically chosen score cutoff. We perform a large-scale evaluation of the approach on four datasets, totaling 152 binding sites. We demonstrate that computed hit rates correlate with hit rates measured experimentally in a previously published NMR-based screening method. Secondly, we show that the in silico fragment screening method can be used to distinguish known druggable and non-druggable targets, including both enzymes and protein-protein interaction sites. Finally, we explore the sensitivity of the results to different receptor conformations, including flexible protein-protein interaction sites. Besides its original aim to assess druggability of different protein targets, this method could be used to identifying druggable conformations of flexible binding site for lead discovery, and suggesting strategies for growing or joining initial fragment hits to obtain more potent inhibitors.