Disable the qubes-update-check service.You can do this from qube manager or using qvm-service.I disable that service everywhere.
The services tab doesn't show services which have the default settings,which can be confusing.Use the drop-down menu to select the service, use the "+" button to addit to the bottom pane, and then deselect the check box. Click OK andyou're done.You can set global settings from the System-GlobalSettings menu item,and there is option to "Disable checking for updates for all qubes"