Introduction Using a self-determination theory framework, we investigated burnout and engagement among PhD students in medicine, and their association with motivation, work-life balance and satisfaction or frustration of their basic psychological needs. Method This cross-sectional study was conducted among PhD students at a university medical centre (n = 990) using an electronic survey on background characteristics and validated burnout, engagement, motivation and basic psychological needs questionnaires. Cluster analysis was performed on the burnout subscale scores to find subgroups within the sample which had similar profiles on burnout. Structural equation modelling was conducted on a hypothesized model of frustration of basic psychological needs and burnout. Results The response rate was 47% (n = 464). We found three clusters/subgroups which were composed of PhD students with similar burnout profiles within the cluster and different profiles between the clusters. Cluster 1 (n = 199, 47%) had low scores on burnout. Clusters 2 (n = 168, 40%) and 3 (n = 55, 13%) had moderate and high burnout scores, respectively, and were associated with low engagement scores. Cluster 3, with the highest burnout scores, was associated with the lowest motivational, engagement, needs satisfaction and work-life balance scores. We found a good fit for the “basic psychological needs frustration associated with burnout” model. Discussion The most important variables for burnout among PhD students in medicine were lack of sleep and frustration of the basic psychological needs of autonomy, competence and relatedness. These add to the factors found in the literature.