To date, we can't deactivate only the update notification. Either you stop update, or you deactivate all notifications. For the latter: go to settings (ctrl+,) then add:
For the latest versions of VS code (I am using version 1.32.2) the parameter "update.channel": "none" is deprecated. To disable updates use "update.mode": "none"
VS Code will no longer check for updates on its own, but you will still be able to update it when you want to, by clicking on the cog at the bottom left:
If you installed VS Code through a package manager (apt/yum/snap...) it will handle the updates and you can turn them off in code: Settings > Update: Mode > none.