Stress and trauma have been shown to have effects that persist across multiple generations. An important mechanism for mediating stress in mammals is the hypothalamic–pituitary–adrenal (HPA) axis. HPA-axis activation during chronic stress conditions can be modelled in male mice using corticosterone water supplementation (PatCORT), which has been previously shown to have transgenerational molecular and behavioural effects. However, the molecular mechanisms transmitting these effects through sperm are not fully understood. In this study we used nanopore long-read sequencing of mouse sperm DNA to investigate potential changes in DNA methylation due to PatCORT. This technique allowed us to characterize the methylation status of more than 18 million CpGs in the genome without bisulphite conversion, thus avoiding bisulphite bias. We observed altered global methylation at imprinted control regions, which are regions with parent-of-origin differential methylation that survive the waves of demethylation that occur during embryogenesis. Moreover, analysis of differentially methylated regions (DMRs) showed that PatCORT leads to decreased methylation in the first intron of the SMAD4 gene. This DMR overlaps a simple repeat and is unlikely to have been identifiable with short-read bisulphite sequencing. This decreased DNA methylation could be altering the expression of SMAD4, which is expressed during embryogenesis and is involved in foetal brainstem development and axon guidance among other things. In conclusion, we have shown that chronic elevation of stress hormone (CORT) in mice leads to changes in sperm DNA methylation that could be inherited by the next generation and thus contribute to intergenerational epigenetic inheritance.