Yes, it’s possible – though will have to be done from within Linux itself – one option is to use command-line like tar and cron.
But if you have open or dynamically changing files, like databases there – you will need proper backup solution, that can handle open files.
I have a mix of physical and ESX boxes here, so I use Acronis Backup for it. They have Linux agent, and as far as I know it can backup folders with snapshots.