ABSTRACT Variants of concern (VOC) in SARS-CoV-2 refer to viruses whose viral genomes differ from the ancestor virus by ≥3 single-nucleotide variants (SNVs) and that show the potential for higher transmissibility and/or worse clinical progression. VOC have the potential to disrupt ongoing public health measures and vaccine efforts. Still, too little is known regarding how frequently new viral variants emerge and under what circumstances. We report a study to determine the degree of SARS-CoV-2 sequence evolution in 94 patients and to estimate the frequency at which highly diverse variants emerge. Two cases accumulated ≥9 SNVs over a 2-week period and one case accumulated 23 SNVs over 3 weeks, including three nonsynonymous mutations in the spike protein (D138H, E554D, D614G). The remainder of the infected patients did not show signs of intra-host evolution. We estimate that in as much as 2% of hospitalized COVID-19 cases, variants with multiple mutations in the spike glycoprotein emerge in as little as 1 month of persistent intra-host virus replication. This suggests the continued local emergence of variants with multiple nonsynonymous SNVs, even in patients without overt immune deficiency. Surveillance by sequencing for (i) viremic COVID-19 patients, (ii) patients suspected of reinfection, and (iii) patients with diminished immune function may offer broad public health benefits. IMPORTANCE New SARS-CoV-2 variants can potentially disrupt ongoing public health measures and vaccine efforts. Still, little is known regarding how frequently new viral variants emerge and under what circumstances. Based on this study, we estimate that in hospitalized COVID-19 cases, variants with multiple mutations may emerge locally in as little as 1 month, even in patients without overt immune deficiency. Surveillance by sequencing for continuously shedding patients, patients suspected of reinfection, and patients with diminished immune function may offer broad public health benefits.