It wants the African Union to intervene and investigate the attacks which seem to be aimed at preventing the militants from communicating.
The Kenyan authorities have not commented on the allegation.
Somali telecoms firm Hormuud issued a statement on Saturday, saying there had been 12 such attacks in the Gedo region disconnecting up to 4,000 people.
It is clear that the Somali government is furious with the Kenyan military.
On the state broadcaster's website, Telecommunication Minister Abdi Anshur Hassan said "an enemy" had openly attacked the Somali economy.