I encountered the same issue and it turns out the IP address was not setup in a firewall rule on Azure, try testing the connection in SQL Server management studio and you will get an error containing a firewall message
this post describes the issue:
Just adding what worked for me. Since I did not obtain the read access to master database, what I did is I created a dummy OLE DB connection (really, whatever OLEDB connection), just to have a connection pop up in QMC. Then I edited the connection string in QMC and added the "Initial catalog" information. Works like charm.
Thanks to patbuchanan for pointing this out, it helped me find a workaround.