You need a ZK-SNARK to make this happen.
That means, you need some sequence of bytes that gets generated (because i assume you'd want to store it on a blockchain) which would need some information that a human has that a computer doesn't.
Consider this.
Assume a human does generate some byte sequence that a computer cannot produce. The human also needs to prove that he/she has provided the correct sequence.
This proof will be an algorithm that a computer can run on the byte sequence.
We have been able to device SNARKs in math because we understand the fundamentals of modulo operations (In case of public private key encryption), because we invented both math and computers.
I am not sure if we have an understanding at that level for any property associated with humans.
What is the underlying logic that creates a fingerprint/DNA? Can that logic be exploited to produce ZK-SNARKs?
PS : I add "ZK" because i'd assume you want to maintain privacy of the human