The emergence of SARS-CoV-2 is responsible for the pandemic of respiratory disease known as COVID-19, which emerged in the city of Wuhan, Hubei province, China in late 2019. Both vaccines and targeted therapeutics for treatment of this disease are currently lacking. Viral entry requires binding of the viral spike receptor binding domain (RBD) with the human angiotensin converting enzyme (ACE2). In an earlier paper, we report on the specific residue interactions underpinning this event. Here we report on the de novo computational design of high affinity antibody variable regions through the recombination of VDJ genes targeting the most solvent-exposed ACE2-binding residues of the SARS-CoV-2 spike protein using the software tool OptMAVEn-2.0. Subsequently, we carry out computational affinity maturation of the designed prototype variable regions through point mutations for improved binding with the target epitope. Immunogenicity was restricted by preferring designs that match sequences from a 9-mer library of human string content (HSC). We generated 60 different variable region designs and report in detail on the top five that trade-off the greatest affinity for the spike epitope (quantified using the Rosetta binding energies) with low immunogenicity scores. By grafting these designed variable regions with frameworks, high-affinity monoclonal antibodies can be constructed. Having a potent antibody that can recognize the viral spike protein with high affinity would be enabling for both the design of sensitive SARS-CoV-2 detection devices and for their deployment as neutralizing antibodies.