A patrol stopped a fishing boat near the Mediterranean port city of Alexandria and arrested three divers, the army spokesman said on his official Facebook page.
He did not give details of the divers' possible motive in severing the link he said belonged to Egypt Telecom, the country's monopoly landline provider.
"The armed forces foiled an attempt and arrested three divers while they were cutting a submarine cable," he said.
It was not immediately clear whether the incident was related to disruptions off Egypt reported by cable operator SEACOM last week that it said hit several lines connecting Europe with Africa, the Middle East and Asia.
SEACOM did not give any explanation for the cuts it said hit its cables and other network systems funneling telecoms traffic backwards and forwards in the early hours of Friday.
Web users have reported slower connections across Egypt since then.
The firm, which carries traffic for other companies, said on Wednesday services had been restored only to report hours later another connection had been cut.
The telecoms infrastructure snaking under the Mediterranean has suffered several disruptions in recent years. In the past, some operators and users have suggested cables had been caught in the propellers of passing ships.
Egypt Telecom said one of its cables had been cut 750 meters off the coast, according to a separate report on state news agency MENA on Wednesday. Services would be restored by Wednesday night, it added.
Crimes rates have been rising across Egypt amid wider disorder triggered by the uprising that unseated Hosni Mubarak in 2011.
(Reporting by Emad Omar and Ulf Laessing; Editing by Andrew Heavens)