Yes, Egypt did shut off the internet, as scattered reports indicated.

Internet monitoring firm Renesys explains:

Confirming what a few have reported this evening: in an action unprecedented in Internet history, the Egyptian government appears to have ordered service providers to shut down all international connections to the Internet. Critical European-Asian fiber-optic routes through Egypt appear to be unaffected for now. But every Egyptian provider, every business, bank, Internet cafe, website, school, embassy, and government office that relied on the big four Egyptian ISPs for their Internet connectivity is now cut off from the rest of the world. Link Egypt, Vodafone/Raya, Telecom Egypt, Etisalat Misr, and all their customers and partners are, for the moment, off the air.

At 22:34 UTC (00:34am local time), Renesys observed the virtually simultaneous withdrawal of all routes to Egyptian networks in the Internet's global routing table. Approximately 3,500 individual BGP routes were withdrawn, leaving no valid paths by which the rest of the world could continue to exchange Internet traffic with Egypt's service providers. Virtually all of Egypt's Internet addresses are now unreachable, worldwide.

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(Via @niubi)