An array of hollow microneedles is constructed of molded plastic, in which a micro-machining technique is used to fabricate the molds used in a plastic microforming process. The molds are detachable and can be re-used. The preferred process for making the plastic arrays of microneedles is a microinjection technique. In the microinjection method, a molten plastic substance is injected between two micro-machined molds that contain microhole and micropillar arrays. Once the desired shape of the microneedle array has been formed, the mold and the plastic material are cooled down. Next, the molds are separated and the plastic microneedle array is detached from the mold structures.