The development of needle-free drug injection systems is of great importance to global healthcare. However, in spite of its great potential and research history over many decades, these systems are not commonly used. One of the main problems is that existing methods use diffusive jets, which result in scattered penetration and severe deceleration of the jets, causing frequent pain and insufficient penetration. Another long-standing challenge is the development of accurate small volume injections. In this paper we employ a novel method of needle-free drug injection, using highly-focused high speed microjets, which aims to solve these challenges. We experimentally demonstrate that these unique jets are able to penetrate human skin: the focused nature of these microjets creates an injection spot smaller than a mosquito's proboscis and guarantees a high percentage of the liquid being injected. The liquid substances can be delivered to a much larger depth than conventional methods, and create a well-controlled dispersion pattern. Thanks to the excellent controllability of the microjet, small volume injections become feasible. Furthermore, the penetration dynamics is studied through experiments performed on gelatin mixtures (human soft tissue equivalent) and human skin, agreeing well with a viscous stress model which we develop. This model predicts the depth of the penetration into both human skin and soft tissue. The results presented here take needle-free injections a step closer to widespread use.