This study was conducted to assess the impacts of using two essential oils, rosemary and ginger, on growing rabbits’ performance, carcass traits, meat composition, blood biochemicals, and the redux status of growing New Zealand White (NZW) rabbits. A total of 120 unsexed NZW rabbits, 42-days-old, were assigned randomly to five experimental groups (n = 24, 6 replicates with 4 rabbits each). The first group received a basal diet (control), the second to fifth groups were dietary supplemented daily with rosemary essential oil (REO) and ginger essential oil (GEO) at doses of 0.25 and 0.5% for each supplementation (REO-0.25, REO-0.5, GEO-0.25, and GEO-0.5), respectively. The growth traits were studied for 7 weeks, from the 7th to the 13th week of the rabbits’ age. The results revealed that final body weight, weight gain, and average daily gain increased significantly (p < 0.01) in the REO-0.5 and GEO-0.5 treatments compared to the control group. Daily feed intake decreased (p = 0.005) in essential oil treatments. Meanwhile, the feed conversion ratio improved significantly (p = 0.001) in REO and GEO at the high doses compared to the control group. The weight percentages of liver and giblets increased (p < 0.001) with both treatments of REO and GEO compared to the control group. The dietary supplementation with REO and GEO did not affect (p > 0.05) the meat composition of Longissimus dorsi and hind leg muscles. Meanwhile, REO and GEO supplementation significantly decreased cholesterol levels in the rabbit meat. Thiobarbituric acid reactive substance concentrations decreased by 10 and 15% in the meat of REO-0.5 and GEO-0.5 treatments, respectively, compared to the other groups. In the same trend, REO and GEO treatments induced a significant (p = 0.001) reduction in the plasma cholesterol concentrations and triglycerides compared to the control. The total antioxidant capacity increased by 7.60% and the malondialdehyde decreased by 11.64% in the plasma of GEO-0.5 treatment than the control. Thus, the dietary supplementation of REO and GEO have a beneficial effect in improving the productivity and meat quality of growing rabbits.