As you know Hyper-V supports VSS so you don’t need to shutdown or save state virtual machine when you want to backup them. But If want to backup virtual machines with Windows Server Backup utility, we need to do small registry trick. You should do some registry changes to support Hyper-V on Windows Server Backup. I created small reg files to do that:

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Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\WindowsServerBackup]
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\WindowsServerBackup\Application Support]
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\WindowsServerBackup\Application Support\{66841CD4-6DED-4F4B-8F17-FD23F8DDC3DE}]
"Application Identifier"="Hyper-V"

Save as HyperVBackup.reg then use this command to import:

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reg import "C:\HyperVBackup.reg"

You can find an article on Microsoft about backing up by Windows Server Backup (KB958662)