The emergence of the SARS-CoV-2 variants of concern has greatly influenced the immune correlates of protection, and there are little data about the antibody threshold concentrations to protect against infection with SARS-CoV-2 Omicron BA.1 or BA.2. We analyzed the antibody responses of 259 vaccinated healthcare workers, some of whom had been previously infected by SARS-CoV-2. The median follow-up was 179 days (IQR: 171–182) after blood collection. We detected 88 SARS-CoV-2 Omicron infections during the follow-up period, 55 (62.5%) with SARS-CoV-2 BA.1, and 33 (37.5%) with SARS-CoV-2 BA.2. A neutralizing antibody titer below 8 provided no protection against a BA.1 infection, a titer of 16 or 32 gave 73.2% protection, and a titer of 64 or 128 provided 78.4% protection. Conversely, the BA.2 infection rate did not vary as a function of anti-BA.2 neutralizing antibody titers. Binding antibody concentrations below 6000 BAU/mL provided no protection against Omicron BA.1 infection, 6000–20,000 BAU/mL provided 55.6% protection, and 20,000 or more provided 87.7% protection. There was no difference in BA.2 infection depending on the binding antibody concentration. Further studies are needed to investigate the relationship between antibody concentrations and infection with the Omicron BA.4/5 variants that are becoming predominant worldwide.