SARS-CoV-2 negatively affects semen characteristics, impairs various biochemical processes in seminal fluid and within spermatogenic cells ultimately leading to male fertility decline. However, the distinct mechanisms, in particular, the role of oxidative stress on the consequences of coronavirus infection, have not been well investigated, which is the purpose of the present study. The standard semen parameters, its pro- and antioxidant system state, as well as the level of sperm DNA fragmentation, were assessed in 17 semen samples of men five months after the coronavirus infection and in 22 age-matched control patients. We determined that the DNA fragmentation rate negatively correlated with the period after coronavirus recovery, as well as seminal fluid superoxide dismutase activity and uric acid level. It was demonstrated that COVID-19 is not always associated with increased DNA fragmentation, allowing them to be considered as two independent factors. Thus, the most significant changes were noted in the samples of men after COVID-19 and abnormal TUNEL results: increased round cell number, decreased seminal fluid’s nitrotyrosine level, and total antioxidant capacity and Zn, as well as an increased 8-hydroxy-2′-deoxyguanosine level within spermatozoa. The data obtained indicate that increased DNA fragmentation and diminished semen quality in men can be the result of an imbalance in semen pro- and antioxidant components after COVID-19.