Elevated levels of brain injury biomarkers have been found primarily in middle-aged or older persons experiencing moderate-to-severe COVID-19 symptoms. However, there is little research in young adults, and there is concern that COVID-19 causes brain injury even in the absence of moderate-to-severe symptoms. Therefore, the purpose of our study was to investigate whether neurofilament light (NfL), glial fibrillary acidic protein (GFAP), tau, or ubiquitin carboxyl-terminal esterase L1 (UCHL1) are elevated in the plasma of young adults with mild COVID-19 symptoms. Twelve participants diagnosed with COVID-19 had plasma collected 1, 2, 3, and 4 months after diagnosis to determine whether NfL, GFAP, tau, and UCHL1 concentrations increased over time or whether plasma concentrations were elevated compared with COVID-19-naïve participants. We also compared plasma NfL, GFAP, tau, and UCHL1 concentrations between sexes. Our results showed no difference between NfL, GFAP, tau, and UCHL1 concentrations in COVID-19-naïve participants and COVID-19-positive participants at any of the four time points (
p
= 0.771). Within the COVID-19-positive participants, UCHL1 levels were higher at month 3 after diagnosis compared to month 1 or month 2 (
p
= 0.027). Between sexes, females were found to have higher UCHL1 (
p
= 0.003) and NfL (
p
= 0.037) plasma concentrations compared to males, whereas males had higher plasma tau concentrations than females (
p
= 0.024). Based on our data, it appears that mild COVID-19 in young adults does not increase plasma NfL, GFAP, tau, or UCHL1.