Microneedle arrays have been given much attention in recent years as a novel way for transdermal drug delivery. In this paper, the orthogonal array design is applied for the first time to optimize the number of microneedles in an array and the inlet pressure suitable for efficient transdermal drug delivery applications. A numerical model of the microneedle array along with the drug reservoir is presented using ANSYS Fluent for different array sizes under four different inlet pressure conditions. Based on these numerical outcomes, an L₁₆ orthogonal Taguchi experiment with two factors, each having four levels, was utilized to determine the optimal change in inlet pressure (∆P) and the number of microneedles (m) for efficient transdermal drug delivery. The output responses accounted for investigation are the flow rate (Q), velocity (v) and pitch (P_t). Taguchi Signal to Noise Ratio (SNR) method is used for the optimization of square microneedle array for efficient drug delivery and the category selected is the larger-the-better of flow rate, velocity and pitch. These output response variables are studied using Analysis of Variance (ANOVA) to determine the relationship between the levels and the responses. The optimal parameters determined via Taguchi Signal to Noise Ratio are pressure of 0.089 MPa and number of microneedles is 49 i.e., 7x7 square microneedle array. It is observed that the change in inlet pressure is the significant parameter to deliver the drug efficiently and to improve the performance of square microneedle array in transdermal drug delivery.