Hybrids between species exhibit plastic genomic architectures that foster phenotypic diversity. Their genomic instability also incurs costs, potentially limiting adaptation. When challenged to evolve in an environment containing a UV mimetic drug, yeast hybrids have reduced adaptation rates compared to parents. We hypothesized that this reduction could result from a faster accumulation of genomic changes, but we found no such association. Alternatively, we proposed that hybrids might lack access to adaptive mutations occurring in the parents, yet, we identified mutations in the same genes (PDR1 and YRR1), suggesting similar molecular adaptation mechanisms. However, mutations in these genes tended to be homozygous in the parents but heterozygous in the hybrids. We hypothesized that a lower rate of loss of heterozygosity (LOH) in hybrids could limit fitness gain. Using genome editing, we demonstrated that mutations display incomplete dominance, requiring homozygosity to show full impact and to circumvent Haldane’s sieve, which favors the fixation of dominant mutations. We used frozen ‘fossils’ to track genotype frequency dynamics and confirmed that LOH occurs at a slower pace in hybrids than in parents. Together, these findings show that Haldane’s sieve slows down adaptation in hybrids, revealing an intrinsic constraint of hybrid genomic architecture that can limit the role of hybridization in adaptive evolution.