In the US, it depends on the consent-to-treat laws of the state. In Washington, under RCW 9.02.100, everybody has a right to reproductive privacy (be it contraceptives or abortions). Under the HIPAA privacy rule, the minor requesting contraceptives would therefore be "the individual", which means that disclosure to others requires consent from the patient. The majority of states similarly allow 16 year olds to request contraceptives. Texas Family Code §32.003 spells out the conditions where a minor can consent to their own medical treatment, which does not include the situation you describe, therefore parental consent would be required (which clearly implies parental notification).
Carey v. Population Services Int'l, 431 U.S. 678 is an important ruling regarding the rights of minors to make their own decisions regarding contraception, but it does not go so far as to declare that minors have a constitutional right to give consent to the requisite medical examination.