The main factor in the turnover of new nurses in Korea is burnout, and a high turnover rate can lead to discontinuation in the nursing profession, due to failure to adapt to the organization. This study aimed to examine the mediating influences of an exchange relationship with the preceptor on the relationship between burnout and job retention intention among new nurses in Korea. Data were collected from 210 new nurses in three general hospitals from 2 May to 30 June 2023. The following statistical analysis were conducted: t-test, ANOVA, the Scheffé test, Pearson’s correlation coefficient analysis, and Hayes Process Macro Model 4 (to test the mediating effect). Burnout was negatively associated with job retention intention (r = −0.54, p < 0.001) and the exchange relationship with the preceptor (r = −0.29, p = 0.001). The exchange relationship with the preceptor was positively associated with job retention intention (r = 0.38, p < 0.001). Furthermore, the mediation analysis indicated that the exchange relationship with the preceptor mediated the relationship between burnout and job retention intention. According to the results, the impact of burnout on the job retention intention was mediated by the exchange relationship with the preceptor. Therefore, to increase the job retention intention of new nurses, developing programs to enhance the exchange relationship with the preceptor are recommended.