This is not an Outlook error. The most common cause is a corrupt registry key in Internet Explorer. The registry key found at
HKEY_Local_Machine\Software\Classes\htmlfile\shell\open\command
is either damaged or corrupt.
To fix it, try resetting Web settings in Internet Explorer. If this does not resolve the issue, set IE as the default browser following the steps in
Set Program Access in Control Panel. If you use a different browser as your default, you need to set IE as the default until you verify the links work in Outlook.
If you uninstalled Chrome (or Firefox) and then received the error, see
Edit Registry, Part 2
In addition to Chrome and Firefox, other HTML rendering and editing programs may take the HTML open command and cause this error. Greg reports UltraEdit is one such program. See
Edit Registry, Part 2 for the fix.