Many rebels were killed in the "major aerial offensive" conducted yesterday, said a ministry statement issued later the same day.
The air strike "completely destroyed an Al-Shebab training
camp," located in the Dinsoor region some 300 kilometres (190 miles) west of Somalia's capital Mogadishu, the statement said.
"Initial reports from the ground confirmed that that four technical vehicles and a weapons store were destroyed."
"At the time of the air strike, the camp had over 300 recruits, many of whom are believed to have perished, with many others suffering injuries," it added.
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There was no immediate reaction from the Shebab, a hardline Islamist and Al-Qaeda-linked rebel group which still controls large parts of southern Somalia.
Kenya promised that "operations of this nature will be sustained into the future" as part of efforts by AMISOM, a 17,700-strong UN-mandated African Union force supporting Somalia's internationally-backed government.
The strike comes amid increased military operations against the Shebab.
AMISOM has requested its size to be boosted to 23,000 troops, with the force now expected to try to push south from Mogadishu and link up with Kenyan troops, denying Shebab access to the sea.
Shebab said it carried out the attack on the Westgate mall, which left at least 67 dead, in retaliation for Kenya's military intervention in Somalia.