Genomic information is a class of Big Data in expanding use thanks to technological developments. Here, we review three categories of ethical risks and challenges associated with genomic information: privacy issues, the management of incidental findings, and challenges in data storage and sharing. First, we need to implement strong mechanisms to protect privacy, but genomic data faces specific risks and we need to acknowledge the possibility of re-identification. Proper usage of genomic information has to be regulated, including recommendations on incidental finding management. Also, clear policies for data sharing and explicit efforts to promote central repositories of genomic data should be established. However, technology and new applications of genetic information will develop fast and we should anticipate potential new risks.