The nanoindentation technique is being widely utilized to measure the mechanical properties of small single crystals of molecular materials. However, all the experiments reported hitherto were performed under quasi-static conditions and at relatively low loading rates. “Will the plastic response change if the tests are performed at high strain rates?” is a question we address in this communication. For this, we have examined the strain rate sensitivity of nanoindentation responses on the major faces of four different molecular crystals: l-alanine, saccharin, p-nitroaniline, and sulfathiazole. Experimental results indicate that the measured hardness values are loading rate insensitive. The possible reasons for this insensitivity and implications for applications in pharmaceutical manufacturing are discussed.