Biomimicry involves taking inspiration from existing designs in nature to generate new and efficient systems. The feathers of birds which form a characteristic herringbone riblet shape are known to effectively reduce drag. This paper aims to optimise the individual constituent structure of a herringbone riblet pattern using a combination of computational fluid dynamics (CFD) and supervised machine learning algorithms to achieve the best possible reduction in drag. Initially, a herringbone riblet design is made by computer aided designing and is parameterised. By randomly varying these parameters, 107 additional designs are made and are subjected to CFD calculations to derive their drag coefficients (Cd). These designs are used to train a supervised learning model which is employed as an alternative to CFD for predicting the Cd of other 10000 randomly generated herringbone riblet designs. Amongst these, the design with the least predicted Cd is considered as the optimised design. The Cd prediction for the optimised design had an error of 4% with respect to its true Cd which was calculated by using CFD. The optimised design of this microstructure can be utilised for drag reduction of aeronautical, automotive or oceanic crafts by integrating them onto their surfaces.