Petroleum hydrocarbons, notably diesel oil, are the main energy source for running amenities in the Antarctic region and are the major cause of pollution in this area. Diesel oil spills are one of the major challenges facing management of the Antarctic environment. Bioremediation using bacteria can be an effective and eco-friendly approach for their remediation. However, since the introduction of non-native organisms, including microorganisms, into the Antarctic or between the distinct biogeographical regions within the continent is not permitted under the Antarctic Treaty, it is crucial to discover native oil-degrading, psychrotolerant microorganisms that can be used in diesel bioremediation. The primary aim of the current study is to optimize the conditions for growth and diesel degradation activity of an Antarctic local bacterium, Arthrobacter sp. strain AQ5-05, using the Plackett-Burman approach and response surface method (RSM) via a central composite design (CCD) approach. Based on this approach, temperature, pH, and salinity were calculated to be optimum at 16.30 °C, pH 7.67 and 1.12% (w/v), respectively. A second order polynomial regression model very accurately represented the experimental figures’ interpretation. These optimized environmental conditions increased diesel degradation from 34.5% (at 10 °C, pH 7.00 and 1.00% (w/v) salinity) to 56.4%. Further investigation of the kinetics of diesel reduction by strain AQ5-05 revealed that the Teissier model had the lowest RMSE and AICC values. The calculated values for the Teissier constants of maximal growth rate, half-saturation rate constant for the maximal growth, and half inhibition constants (μmax, Ks, and Ki), were 0.999 h−1, 1.971% (v/v) and 1.764% (v/v), respectively. The data obtained therefore confirmed the potential application of this cold-tolerant strain in the bioremediation of diesel-contaminated Antarctic soils at low temperature.