Does Data Migration Advisor migrate system databases? I would like to know if Data Migration Assistant copies system databases (master, model, msdb) into the new server.
No, because the Data Migration Assistant helps you to move from SQL Server to Azure SQL.

Azure SQL is a different product and thus the system databases are not the same. You will only be able to access the master database on your Azure SQL deployment. That being said, there really isn't anything you will be missing by not moving those over, since most functions of msdb aren't available on Azure SQL in the same way anyways. 

From the documentation:


  For Azure SQL Database single databases and elastic pools, only master
  Database and tempdb Database apply.