Duplicated genes provide the opportunity for evolutionary novelty and adaptive divergence. In many cases, having more gene copies increases gene expression, which might facilitate adaptation to stressful or novel environments. Conversely, overexpression or misexpression of duplicated genes can be detrimental and subject to negative selection. In this scenario, newly duplicate genes may evade purifying selection if they are epigenetically silenced, at least temporarily, leading them to persist in populations as copy number variations (CNVs). In animals and plants, younger gene duplicates tend to have higher levels of DNA methylation and lower levels of gene expression, suggesting epigenetic regulation could promote the retention of gene duplications via expression repression or silencing. Here, we test the hypothesis that DNA methylation variation coincides with young duplicate genes that are segregating as CNVs in six populations of the three‐spined stickleback that span a salinity gradient from 4 to 30 PSU. Using reduced‐representation bisulfite sequencing, we found DNA methylation and CNV differentiation outliers rarely overlapped. Whereas lineage‐specific genes and young duplicates were found to be highly methylated, just two gene CNVs showed a significant association between promoter methylation level and copy number, suggesting that DNA methylation might not interact with CNVs in our dataset. If most new duplications are regulated for dosage by epigenetic mechanisms, our results do not support a strong contribution from DNA methylation soon after duplication. Instead, our results are consistent with a preference to duplicate genes that are already highly methylated.