The fate of those on board – believed to be 14 people – is unknown, Colonel Cyrus Oguna said.
Both aircraft were part of a contingent being sent to reinforce the African Union (AU) force in Somalia.
A third helicopter on the same mission made an emergency landing in Mount Kenya on Sunday.
Its passengers have been rescued, Col. Cyrus Oguna said.
Only one of the four Russian-made helicopters en route to Somalia had made a scheduled refuelling stop on Sunday in the Kenyan town of Garissa.
The wreckage of the two missing helicopters was spotted on Mount Kenya – Africa’s second-highest peak at 5,199 metres (17,057 feet) – by wildlife officers, Kenya’s Daily Nation newspaper reports.
A Kenyan army team is on the way to the site of the crash, said Col. Cyrus Oguna.
One helicopter has been completely destroyed and the other partially, he said.
The combat helicopters came down as they were flying from Uganda to Somalia to take part in an AU-led offensive to capture the port city of Kismayo from the militant Islamist group al-Shabab, correspondents say.
Ugandan troops form the bulk of the nearly 17,000-strong AU force in Somalia, where they are supporting the UN-backed government.
Although it has lost ground in the past year, al-Shabab, which has joined al-Qaeda, still controls many southern and central areas.
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