The al-Qaeda-linked al-Shabab group has given firms 15 days to shut down mobile internet and fiber optic services, which are due to launch soon.
Those who do not comply would be seen as “working with the enemy” and dealt with according to Islamic law, it said.
Correspondents say the group often executes those it accuses of spying for Somalia’s government or Western powers.
Al-Shabab was driven out of the capital, Mogadishu, in August 2011, but still controls many southern and central areas of the country.
According to Internet World Stats, in June 2012 Somalia had more than 126,000 internet users, about 1.2% of the population.
Analysts say this is set to grow as more internet services come to Mogadishu, with a returning Diaspora and the imminent connection to fiber optic cables.
The BBC’s Mohamed Moalimu in Mogadishu says telecom firms have begun advertising cut-price deals ahead of the broadband launch.
They currently provide internet services via dial-up or satellite.
Al-Shabab’s statement was issued on the Facebook page of its Al-Andalus radio station.
“Services known as mobile internet and fiber optics must be stopped in Somalia,” it said.
“Any firm or individual who does not comply will be seen to be working with the enemy and will be dealt with in accordance with Islamic law,” it said.
African Union (AU) and government troops have been battling Al-Shabab fighters for years.
They have been driven out of some key cities, but still hold sway over many small towns and much of rural Somalia where they have imposed a strict version of Sharia.