Ammodaucus leucotrichus exhibits promising pharmacological activity, hinting at anti-inflammatory and anti-arthritic effects. This study investigated seed extracts from Ammodaucus leucotrichus using methanol and n-hexane, focusing on anti-inflammatory and anti-arthritic properties. The methanol extract outperformed the n-hexane extract and diclofenac, a reference anti-inflammatory drug, in trypsin inhibition (85% vs. 30% and 64.67% at 125 μg/mL). For trypsin inhibition, the IC50 values were 82.97 μg/mL (methanol), 202.70 μg/mL (n-hexane), and 97.04 μg/mL (diclofenac). Additionally, the n-hexane extract surpassed the methanol extract and diclofenac in BSA (bovine serum albumin) denaturation inhibition (90.4% vs. 22.0% and 51.4% at 62.5 μg/mL). The BSA denaturation IC50 values were 14.30 μg/mL (n-hexane), 5408 μg/mL (methanol), and 42.30 μg/mL (diclofenac). Gas chromatography–mass spectrometry (GC–MS) revealed 59 and 58 secondary metabolites in the methanol and n-hexane extracts, respectively. The higher therapeutic activity of the methanol extract was attributed to hydroxyacetic acid hydrazide, absent in the n-hexane extract. In silico docking studies identified 28 compounds with negative binding energies, indicating potential trypsin inhibition. The 2-hydroxyacetohydrazide displayed superior inhibitory effects compared to diclofenac. Further mechanistic studies are crucial to validate 2-hydroxyacetohydrazide as a potential drug candidate for rheumatoid arthritis treatment.