An injector for delivering an injectate into the myocardium of the heart may be implemented as a catheter or a handheld unit. The injector includes a body, a stabilizer secured to a distal end of the body, and a needle that may be controllably advanced from the distal end of the body. The stabilizer stabilizes the distal end of the body relative to the myocardium while the heart beats. An enlarged region disposed along the needle prevents the needle from being advanced into the myocardium beyond a desired penetration depth. To make an injection, the physician brings the distal end of the body in proximity to the myocardium, actuates the stabilizer to stabilize the distal end relative to the myocardium, and advances the needle into the myocardium. Advancement of the needle is impeded by the enlarged region, thereby placing the needle tip at the desired penetration depth for the injection.