The Somalia-based terrorists claimed the attack killed 15 soldiers, according to US extremism monitor SITE.
The group also published the claims in a statement shared through its media affiliate Radio Andalus.
The soldiers died after their vehicle, a Toyota Landcruiser, ran over an improvised explosive device (IED) near the Somali town of Dhobley.
The soldiers were in a convoy that was returning to their camp on the outskirts of Dhobley, Lower Jubba region, from Dadaab camp in northern Kenya.
President Kenyatta, while reacting to the attack, on Monday vowed that Kenyan military would stay in Somalia until the Shabaabs are defeated.
"Earlier today, I was appalled and saddened to learn that we had lost nine young patriots to a cowardly terrorist attack in Somalia," he said in a statement.
"These men gave their lives for their country, and for peace; we must, and we will, honour their service, their sacrifice and their valour."
He added: “The mission for which they gave everything will continue until the evil terrorists of Al Shabaab are defeated, and the people of Somalia are safe once more. We owe victory to the fallen. You may be sure we will win, for we have right and might on our side.
Al-Shabaab is fighting to overthrow the internationally backed government in Mogadishu and install an Islamic caliphate that frowns upon anything associated with the West, including football.
An intelligence report released by the Kenyan security agencies in the wake of the blast warned of more attacks and called for vigilance.
“The lull witnessed in the recent past points to AS (Al-Shabaab) planning phase to deploy IED in the upcoming Ramadhan period,” the report says.
“Based on the past experience, AS (Al-Shabaab) deploy IEDs in the theatre by consignments and it’s very likely that similar consignments have been deployed...”
Al-Shabaab declared war on Kenya when Nairobi deployed forces to help stabilise the Horn of Africa nation in 2011.
While they gave up on field combat, the terrorists have been launching sporadic attacks on KDF and African Union Mission in Somalia (Amisom) convoys and camps.
The group, a member of the Al-Qaeda global terror network, was pushed out of the Somali capital, Mogadishu, in 2011 — and subsequently other towns and cities — by Amisom forces.
But the Islamists still hold sway in large parts of the countryside and launch regular gun and bomb attacks on government, military and civilian targets in Mogadishu.