If you are protecting Microsoft SQL Server 2012 and later databases, you can install and use Data Protection for SQL Server on Windows Server 2008 R2 Server Core SP1 and later.
Server Core is a minimal and low-maintenance server environment where you can run the minimum services necessary to maintain Windows Server 2008 and later. You can install and operate Data Protection for SQL Server in this minimal server environment.
Because of the minimal environment, only the command-line interface is available for Data Protection for SQL Server on Windows Server Core. Also, if you use Windows Installer (MSI) to install Data Protection for SQL Server, only the unattended mode is supported.