COVID-19 Vaccine Protection Act This bill requires enhanced vetting of Chinese nationals in the United States on student or exchange visitor visas and temporarily stops the issuance of such visas to Chinese nationals. The Department of Homeland Security (DHS) shall conduct comprehensive background checks on any Chinese national (unless the individual is enrolled in elementary or secondary school) residing in the United States on an F, M, or J visa to determine if the individual is a national security threat or attempting to illegally obtain COVID-19 (i.e., coronavirus disease 2019) vaccine research. When performing such background checks, DHS shall consult with the Department of State, the Department of Justice, the Federal Bureau of Investigation, the Cybersecurity and Infrastructure Security Agency, U.S. Citizenship and Immigration Services, the Office of the Director of National Intelligence, and the Department of Health and Human Services. DHS shall complete all such background checks within 120 days of this bill's enactment and may extend the deadline by 60 days if necessary. The State Department may not issue F, M, or J visas to Chinese nationals until DHS has reported to Congress the completed results of the background checks. DHS shall continuously vet any Chinese national holding an F, M, or J visa who has access to any COVID-19-related research, unless the individual is enrolled in elementary or secondary school.