Inclusion Criteria: 1. Female or male adults ( ≥ 18 years old) 2. Part A only: Confirmed diagnosis of Type I HAE due to C1-INH deficiency confirmed by genotyping of the SERPING1 gene Part B only: Confirmed diagnosis of Type I or II HAE due to C1-INH deficiency confirmed by genotyping of the SERPING1 gene 3. Currently using an HAE medication regimen that consists of a routine long-term prophylactic treatment for at least 6 months prior to enrollment or an on-demand therapy regimen for a documented attack frequency of at least 4 attacks within the last 12 months prior to enrollment or at least 2 attacks within the last 6 months prior to enrollment 4. Trained in self-administering acute attack treatment and is able to adequately manage acute attacks in a home setting 5. Willingness to abstain from consumption of alcohol for at least 52 weeks post BMN 331 infusion and to use highly effective contraception Exclusion Criteria: 1. Evidence of active or chronic infection, including severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), or any immunosuppressive disorder 2. Contraindication to using glucocorticosteroids GCS, including a diagnosis of glaucoma or untreated osteoporosis 3. Active malignancy (except non-melanoma skin cancer) autoimmune, metabolic (i.e., diabetes), hematologic, cardiac, or renal disease that is of clinical significance defined as requiring regular medical attention and treatment 4. Prior gene therapy treatment 5. Prior use of high-dose attenuated androgens in the last 1 year prior to the study 6. History or current clinically relevant liver disease (eg, nonalcoholic steatohepatitis \[NASH\], or chronic viral hepatitis B or C \[HBV or HCV\] or autoimmune hepatitis) 7. Have a history or are at risk for clinically significant thromboembolic events (TEE) , or known underlying risk factor for thrombosis including thrombotic microangiopathy (TMA)