Question: Is it legal to have a minor tested for drugs without their parents permission?
Answer: The United States Constitution protects adults and children from illegal searches (the Fourth Amendment).
Taking blood or urine from a person's body to test for drugs can be considered a search. So, it really depends on WHO is making the juvenile take the drug test; and WHY the drug test is being done.
For example, the United States Supreme Court has held that a school can require mandatory drug testing for athletes in school programs and that this does not violate a student's constitutional rights. However, a teacher could not simply walk up to a student for no reason whatsoever and start singling out students to take drug tests.