The emergence of escape variants of SARS-CoV-2 carrying mutations in the spike protein poses a challenge for therapeutic antibodies. Here, we show that through the comprehensive engineering of the variable region of the neutralizing monoclonal antibody 5A6, the engineered antibody, 5A6CCS1, is able to neutralize SARS-CoV-2 variants that escaped neutralization by the original 5A6 antibody. In addition to the improved affinity against variants, 5A6CCS1 was also optimized to achieve high solubility and low viscosity, enabling a high concentration formulation for subcutaneous injection. In cynomolgus monkeys, 5A6CCS1 showed a long plasma half-life and good subcutaneous bioavailability through engineering of the variable and constant region. These data demonstrate that 5A6CCS1 is a promising antibody for development against SARS-CoV-2 and highlight the importance of antibody engineering as a potential method to counteract escape variants.