Major depressive disorder (MDD) is a leading contributor to the global burden of disease. However, the causal relationship of risk factors, such as genetic predisposition or experience of augmented stress, remain unknown. Numerous studies in humans and rodents have implicated brain‐derived neurotrophic factor (BDNF) in MDD pathology, as a genetic risk factor and a factor regulated by stress. Until now, the majority of preclinical studies have employed genetically modified mice as their model of choice. However, mice display a limited behavioural repertoire and lack expression of circulating BDNF, which is present in rats and humans. Therefore, heterozygous BDNF (BDNF+/−) rats were tested for affective behaviours and accompanying expression of key genes associated with affective disorders in the brain. We found that BDNF+/− rats, which have reduced BDNF levels in brain and plasma, displayed symptoms of anhedonia, a core symptom of MDD, and anxiety‐like behaviour, but no behavioural despair or cognitive impairments. This was accompanied by changes in the expression of genes that are implicated in modulation of the stress response and affective disorders. Hence, glucocorticoid receptor, neuregulin 1 and disrupted‐in‐schizophrenia 1 gene expression were upregulated in the prefrontal cortex of BDFN+/− rats, whereas FK506 binding protein 5 levels were decreased in the hippocampus. We conclude that a reduction in BDNF levels alters expression of genes associated with affective disorders, which may contribute to the development of depressive‐like symptoms.