Bacterial antibiotic resistance, a global health threat, is caused by plasmid transfer or genetic mutations. Quinolones are important antibiotics, partially because they are fully synthetic and resistance genes are unlikely to exist in nature; nonetheless, quinolone resistance proteins have been identified. The mechanism by which plasmid-borne quinolone resistance proteins promotes the selection of quinolone-resistant mutants is unclear. Here, we show that QnrB increases the bacterial mutation rate. Transcriptomic and genome sequencing analyses showed that QnrB promoted gene abundance near the origin of replication (oriC). In addition, the QnrB expression level correlated with the replication origin to terminus (oriC/ter) ratio, indicating QnrB-induced DNA replication stress. Our results also show that QnrB is a DnaA-binding protein that may act as an activator of DNA replication initiation. Interaction of QnrB with DnaA promoted the formation of the DnaA-oriC open complex, which leads to DNA replication over-initiation. Our data indicate that plasmid-borne QnrB increases bacterial mutation rates and that genetic changes can alleviate the fitness cost imposed by transmitted plasmids. Derivative mutations may impair antibiotic efficacy and threaten the value of antibiotic treatments. Enhanced understanding of how bacteria adapt to the antibiotic environment will lead to new therapeutic strategies for antibiotic-resistant infections.