The attack began with suicide truck bombers blasting their way into the camp.
The attack on the Kenya Defence Forces (KDF) base at Kolbiyow, close to the Kenyan border in Somalia's Lower Juba region, began with suicide truck bombers blasting their way into the camp, followed by militants attacking from different directions.
Shabaab claimed in a statement to have overrun the base, captured military vehicles and equipment and to have killed scores of Kenyan soldiers.
"Fighters have taken control of the base and the overall Kolbiyow area after massacring the Kenyan infidels," the statement said.
KDF spokesman Paul Njuguna denied the base had been overrun, but gave no casualty figures.
"We are engaging the enemy and we have actually repulsed them, but it is ongoing," Njuguna said.
Shabaab frequently overstates the death toll from its attacks while Kenya commonly underplays its losses.
In January last year a Kenyan base at El-Adde was attacked and overrun by Shabaab fighters who claimed to have killed over 100 Kenyan soldiers. The government never gave its own toll.
The Shabaab, which once controlled much of Somalia, is fighting to overthrow the internationally-backed government in Mogadishu.
It launches regular attacks on government, military and civilian targets and has carried out a series of deadly assaults against foreign soldiers deployed in Somalia as part of an African Union force.
On Tuesday at least 28 people were killed when Shabaab bombers and fighters attacked a hotel in the capital.