Restrict access to Edition- or instance-specific databases
There is no way to prevent a client software from accessing a SQL Server instance when correct credentials are supplied. 

SQL Server Management Studio is the same product for all editions (actually, starting from SQL Server 2016, it is a separate product which ships separately from the engine).

Your only option to prevent users from accessing one of the instances in your server is granting permissions only to the people entitled to access the data.