A wide range of SARS-CoV-2 neutralizing monoclonal antibodies (mAbs) were reported to date, most of which target the spike glycoprotein and in particular its receptor binding domain (RBD) and N-terminal domain (NTD) of the S1 subunit. The therapeutic implementation of these antibodies has been recently challenged by the emerging SARS-CoV-2 variants, harboring an extensively-mutated spike versions. Consequently, the re-assessment of mAbs, previously reported to neutralize the original early-version of the virus, represents an assignment of high priority. With respect to the evolving mutations in the virus spike RBD, we evaluated the aptitude of four previously selected mAbs, targeting distinct epitopes, to bind RBD versions harboring individual mutations at positions 501, 477, 484, 439, 417 and 453. Mutations of these residues represent the prevailing worldwide distributed modifications of the RBD, previously reported to mediate escape from antibody neutralization. Additionally, the in vitro neutralization efficacies of the four RBD-specific mAbs, as well as two NTD-specific mAbs, were evaluated against two frequent SARS-CoV-2 variants of concern (VOCs): (i) the B.1.1.7 variant, emerged in the UK and (ii) the B.1.351 variant, emerged in South Africa. B.1.351, was previously suggested to escape many therapeutic mAbs, including those authorized for clinical use. The results of the present study, clearly indicate that in spite of mutation accumulation in the spike of the virus, some neutralizing mAbs preserve their potency to combat SARS-CoV-2 emerged variants. In particular, the previously reported highly potent MD65 mAb is shown to retain its ability to bind the prevalent novel viral mutations and to effectively neutralize the B.1.1.7 and B.1.351 variants of high clinical concern.