False discovery rate (FDR) control is highly desirable in several high-dimensional estimation problems. While solving such problems, it is observed that traditional approaches such as the Lasso select a high number of false positives, which increase with higher noise and correlation levels in the dataset. Stability selection is a procedure which uses randomization with the Lasso to reduce the number of false positives. It is known that concave regularizers such as the minimax concave penalty (MCP) have a higher resistance to false positives than the Lasso in the presence of such noise and correlation. The benefits with respect to false positive control for developing an approach integrating stability selection with concave regularizers has not been studied in the literature so far. This motivates us to develop a novel upper bound on false discovery rate control obtained through this stability selection with minimax concave penalty approach.