This investigation was conducted to assess the baseline level of sperm DNA fragmentation (SDF) in a cohort of patients presenting chromosomal rearrangements (nine reciprocal translocations and two inversions). In a separate experiment, a dynamic analysis to calculate the rate of SDF (rSDF), after a varying period of sperm storage (0 h, 1 h, 4 h, 8 h and 24 h) at 37 °C, was performed. Results were compared with eight fertile donors. Different experimental approaches to assess SDF, such as terminal transferase dUTP nick-end labelling (TUNEL), sperm chromatin structure assay (SCSA) and sperm chromatin dispersion test (SCDt), were used. No differences for the baseline level of SDF were found. Carriers of reorganized genomes showed statistically higher levels of SDF than did control donors (p = 0.025 for TUNEL; p = 0.022 for SCSA; p = 0.014 for SCDt). However, 54.5% (6/11) of the patients presented values similar to those of control donors. There was no significant difference in rSDF (p = 0.34). Nevertheless, the results suggest that a high variability for SDF and rSDF exists in these patients. Routine analysis of SDF and rSDF should be considered in patients presenting rearranged genomes to determine fertility status for assisted reproductive techniques (ART) purposes.