Nowadays, in most industrial units, biodiesel is produced through transesterification of edible oil and methanol using homogeneous basic catalysts in stirred-tank reactors. The drawbacks of this method include the high cost of feedstock, long reaction time, high energy consumption, and excessive wastewater production. The present study investigated an alternative process, in which biodiesel was produced from indigenous, inedible Norouzak (Salvia leriifolia) oil in the presence of choline hydroxide (ChOH) as an ionic liquid catalyst in a microchannel reactor. Taking into account catalyst concentration, methanol-to-oil volume ratio, and reaction time as the independent variables, Response Surface Methodology (RSM) with a Box-Behnken experimental design was used to determine the optimal reaction efficiency as the response. An efficiency of 93.36% was predicted by the model for a catalyst concentration of 6.11 wt%, methanol-to-oil volume ratio of 0.37, and reaction time of 12.48 min. By conducting experiments under these conditions, an efficiency of 96.8% was obtained. In comparison with the results of previous studies in which ChOH was used as the transesterification catalyst, employing the microchannel reactor in this study reduced the reaction time to less than 0.1 that of a mechanical stirrer. Moreover, the energy consumption was 32 times lower than that of a mechanical stirrer. The use of ChOH instead of KOH in a microchannel reactor increased efficiency by 1.9–4.9%. Compared to heterogeneous catalysts, ChOH can reduce the catalyst and alcohol consumption by at least 29% and 30%, respectively.