There was disruption to 70% of the nationwide network in Egypt, and India suffered up to 60% disruption.
UK firms such as British Airways have told the BBC that call centres have been affected by the outage.
Industry experts said it could take up to one week to repair the damaged cables and resume full service.
International telephone calls, which have also been affected, are being rerouted to work around the problem.
Disruption also occurred in the United Arab Emirates (UAE), Kuwait and Saudi Arabia, reported the Associated Press.
In Dubai, at least two internet service providers (ISPs) were affected.
An official at the provider, DU, told AP that a fault in a network between Alexandria, Egypt, and Palermo, Italy, was to blame.
DU issued a statement to alert customers to "a degradation in internet services and international voice calls for some customers during peak times".
The company said it was due to "cuts in two international submarine cable systems in the Mediterranean Sea this morning (Wednesday).
"We are working actively with the submarine cable system operators (FLAG Telecom and SEA-ME-WE 4) to ascertain the reasons for the cables being cut," it said.
FLAG Telecoms operate the Fiber-Optic Link Around the Globe (FLAG), a 28,000km (17,400 mile) long submarine communications cable.
SEA-ME-WE 4, or the South East Asia-Middle East-West Europe 4 project, is a submarine cable system linking South East Asia to Europe via the Indian subcontinent and the Middle East.
Neither of the cable operators have confirmed the cause or location of the outage but some reports suggest it was caused by a ship's anchor near the port of Alexandria in Egypt.
One Indian internet service provider, Videsh Sanchar Nigam Ltd (VSNL), linked the problems in India to the disruption in Egypt.
"Information technology companies, software companies and call centres that provide online services to the UK or the US east coast are the worst affected," Rajesh Chharia, president of the Internet Service Providers' Association of India, told Agence France-Presse (AFP).
India is the world leader in offshore outsourcing, with the remote servicing of IT or other business processes worth an estimated £24bn.
AFP also reported disruption to telecommunications in Bangladesh and Sri Lanka.
Egypt's Telecommunications Ministry said it would probably take several days for internet services to return to normal following the disruption on Wednesday.
Emergency teams were trying to find alternative communication routes, including satellites, AP was told.
The ministry's Rafaat Hindy said: "Despite this being an international cable affecting many Gulf and Arab countries, we are closest to it and so we have a lot of responsibility.
"We are working as fast as we can."