Currently SQL Data Sync service only works with Azure SQL Databases, SQL Server, SQL Express and LocalDB databases.
However you can use Sync Framework to build your own solution. Please read this article to know how. This is another related article. If you finally decide to build your own implementation of Azure Data Sync please take in consideration these recommendations.
Another option you have is to sync between a MySQL (on-premises) and a subordinate server running on MySQL Database on Azure. See this documentation.