If it were a scheduled downtime - probably not so much panic. If it were unscheduled downtime, panic on a wide scale, and then the whole Internet would crazy with the outage theories and news items.
Everyone would blame their local provider for an outage. There would be extensive cursing.
Everyone would start to find something else to do while constantly checking phones, restarting routers, calling friends, calling the electric company, etc. The IT company of every major company of the world would have people showing up in the doorway. People would learn to use the phone - mostly to complain.
After a whole 24hours when the internet resumes business and life as normal would resume. However, this is when the real stuff happens.
The economic impacts of the closure would be assessed. Business didn't happen.
Everyone would be demanding an investigation.
Everyone would be blaming somebody else.
There would be multiple statements of "Not to worry, we're investigating this incident thoroughly" as all the world leaders communicated and realized that this was truly a worldwide event.
Technological consultants would be called in to determine how this could even be possible.
Comics would be written.
Comedians would have a new script.
Story lines and movies would be written.