Thrombosis is an extremely dangerous complication in elderly patients with COVID-19. Since the first months of the pandemic, anticoagulants have been mandatory in treatment protocols for patients with COVID-19, unless there are serious contraindications. We set out to discover if genetic thrombophilia factors continue to play a triggering role in the occurrence of thrombosis in patients with COVID-19 with prophylactic or therapeutic anticoagulants. We considered the following genetic markers as risk factors for thrombophilia: G1691A in the FV gene, C677T and A1298C in the MTHFR gene, G20210A and C494T in the FII gene, and (-675) 4G/5G in the PAI-I gene. In a cohort of 176 patients, we did not obtain a reliable result indicating a higher risk of thrombotic complications when taking therapeutic doses of anticoagulants in carriers of genetic markers for thrombophilia except the C494T mutation in the FII gene. However, there was still a pronounced tendency to a higher incidence of thrombosis in patients with markers of hereditary thrombophilia, such as FV G1691A and FII G20210A mutations. The presence of the C494T (Thr165Met) allele in the FII gene in this group of patients showed a statistically significant effect of the mutation on the risk of thrombotic complications despite anticoagulant therapy.