Background: Impurity profiling is now receiving critical attention from regulatory authorities. For trace level quantification of potential genotoxic impurities (PGIs), conventional analytical techniques like high-performance liquid chromatography (HPLC) and gas chromatography (GC) are inadequate; consequently, there is a great need to apply hyphenated analytical techniques to develop sensitive analytical methods for the analysis of pharmaceuticals. Methods: A selective and sensitive liquid chromatography-tandem mass spectrometry (LC-MS/MS) method was developed for the simultaneous determination of (4-sulfamoylphenyl)hydrazine hydrochloride (SHH) and (4-methyl-acetophenone)para-sulfonamide phenylhydrazine hydrochloride (MAP) PGIs in celecoxib active pharmaceutical ingredient (API). The LC-MS/MS analysis of SHH and MAP PGIs was done on Symmetry C18 (150 mm × 4.6 mm, 3.5 μm) analytical column, and the mobile phase used was 5.0 mM ammonium acetate-acetonitrile in the ratio of 30:70 (v/v). The flow rate used was 0.7 mL/min. Triple quadrupole mass detector coupled to positive electrospray ionization operated in multiple reaction monitoring (MRM) mode was used for the quantification of SHH and MAP PGIs. The method was validated as per International Conference on Harmonization (ICH) guidelines and was able to quantitate both SHH and MAP PGIs at 1.0 ppm with respect to 10 mg/mL of celecoxib. Results: The proposed method was specific, linear, accurate, precise, and robust. The calibration curves show good linearity between the concentration range of 0.06 and 7.5 ppm for both SHH and MAP PGIs. The correlation coefficient obtained was >0.9998 in each case. The method has very low limit of detection (LOD) and limit of quantification (LOQ). The obtained LOD and LOQ values were 0.02 and 0.06 ppm, respectively, for both SHH and MAP PGIs. For both the PGIs, excellent recoveries of 95.0% to 104.0% were obtained at a concentration range of 0.06 to 3.0 ppm. The developed method was also applied to determine the SHH and MAP PGIs in three formulation batches of celecoxib. Conclusions: The proposed method is simple and accurate and is a good quality control tool for the simultaneous quantitative determination of SHH and MAP PGIs at very low levels in celecoxib during its manufacturing.