Digitalization of Russian healthcare leads to an increase of digital medical data, which eventually becomes Big Data and requires secure ways to collect, process, store and use such information. In this article, the authors analyze legal acts that govern ways to protect medical information in digital form, as well as those that establish the legal regime of personal data. The authors draw attention to the risks of re-identification of anonymized medical data and difficulties to comply with some requirements of the personal data legislation in use of Big Data technologies. In discussion on liability for offences and crimes in the sphere of computer information, the authors propose to consider healthcare information systems containing personal data as objects of critical information infrastructure of the Russian Federation. Such regime would allow to charge unlawful access to the information contained and other criminal acts under Article 274¹ of the Criminal Code of the Russian Federation. Prevalence of information and communication technologies as a method of encroachments on the digital medical data, and ultimately an intrusion into privacy, leads authors to the conclusion about expediency of addition of Article 137 of the Criminal Code of the Russian Federation with the relevant aggravating circumstance.