The alleged incursion took place on Monday during clashes in southern Somalia between the army and fighters loyal to the leader of Jubbaland, a semi-autonomous Somalian state. Nairobi said Somali troops destroyed Kenyan properties on the border.
Kenya has accused Somalia of violating its territorial integrity and demanded it cease such breaches in an escalating feud that Washington says is undermining the fight against militant group al Shabab.
The alleged incursion took place on Monday when clashes broke out in southern Somalia between the Somali army and fighters loyal to Ahmed Madobe, leader of Jubbaland, which is one of Somalia's five semi-autonomous states.
The Nairobi government, in a statement on Wednesday, said Somali army troops had destroyed the properties of Kenyans in the town of Mandera, which lies along the shared border.
The Somali information minister in Mogadishu did not immediately respond to a request for comment.
The fighting has regional dimensions in East Africa.
Madobe is an ally of Kenya, which helped build his forces, but is detested by neighbouring Ethiopia, which has backed Somalia's central government.
Both Kenya and Ethiopia have troops in Somalia as part of an African Union-led peacekeeping force which, along with the Somali federal government and local states, are supposed to be fighting al Shabab's insurgency.
The US warned last week that the rivalries were distracting from the war on the al Qaeda-linked group, which has been battling the internationally recognised Somali government since 2008.
During the clashes on Monday, Kenya said Somali soldiers "engaged in aggressive and belligerent activities by harassing and destroying properties of Kenyan citizens" in Mandera.
"This action amounts to an unwarranted attack by foreign soldiers with the intention of provoking Kenya," added the government statement, which demanded Somalia "cease and desist" from such acts.