The inappropriate use and indiscriminate disposal of antibiotics has become a menace worldwide. The incomplete removal of these contaminants from wastewater treatment plants has also contributed to this. This study presents the biodegradation of two veterinary antibiotics; ciprofloxacin (CIP) and enrofloxacin (ENRO). Kinetics models were explored to understand the dynamics of biodegradation in an anaerobic digestion process. This was carried out in batch reactors under various operating conditions: pH, organic loading rate (OLR), and antibiotic concentration. The influence of the parameters was investigated using a response surface methodology (RSM) based on the Box–Behnken experimental design of 15 runs. The data obtained were fitted on a polynomial function model. OLR and pH exhibited a synergistic and antagonistic effect in the response models developed, with a high correlation regression coefficient (R2; 0.9834–0.9875) close to 1 at a 95% confidence level. The optimum conditions obtained from the RSM numerical optimization were pH (6), OLR (2 kgCOD·m−3·days−1), and an antibiotic concentration of 75%, which gave the removal of CIP, ENRO, and COD, respectively, as 80%, 83%, and 73% at a desirability function of 85%. The kinetics study shows that the biodegradation of antibiotics was well fitted on a first-order model (R2; 0.9885–0.9978) with rate constants ranging from 0.0695 to 0.96 days−1.