That is a standard that any injection/vaccination is unlikely to meet.
The standard flu shot is commonly thought (and been shown in some studies (non-conclusive) to have a 1 in 500,000 chance of triggering
Guillain-Barré syndrome (GBS)..
Most shots also show some risk of severe allergic reaction, though again, this would be quite rare.
I say that not to be alarmist in any way; those risks are really very, very low.
But zero-risk is not likely attainable.
As of January 20, 2021, a total of 24,135,690 cases of coronavirus disease 2019 (COVID-19) and 400,306 associated deaths had been reported in the United States.
www.cdc.gov
From the above:
During December 21, 2020–January 10, 2021, monitoring by the Vaccine Adverse Event Reporting System detected 10 cases of anaphylaxis after administration of a reported 4,041,396 first doses of Moderna COVID-19 vaccine (2.5 cases per million doses administered). In nine cases, onset occurred within 15 minutes of vaccination. No anaphylaxis-related deaths were reported.
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A previous analysis of the Pfizer-BioNTech COVID-19 vaccine, also an mRNA vaccine, estimated an initial rate of 11.1 cases per million doses administered after receipt of the first dose of the Pfizer-BioNTech vaccine
That's a pretty low risk-profile. But not zero.