Who collected the genetic data? A hospital? A research lab? The data subject should contact the data controller who collected the data and exercise the right of erasure according to the privacy notice.
The data controller will verify if the request can be fulfilled or not. Member States may introduce specific limitations to data subjects' rights (even to the sensitive data under Article 9 GDPR) in order to protect scientific research programs, for example. So maybe there is a legitimate base to keep the genetic data in the database without the consent of the data subject.
Controller processing genetic data should have a Data Protection Officer (DPO), so the data subject may contact the DPO in order to have clarification.