The soldiers were attacked while transporting food supplies to a military camp across the border, the Nation newspaper said, adding that several other soldiers were also wounded.
Kenyan military officials only confirmed that some of their troops were hurt and said one of the attackers was killed.
"Our officers are in hot pursuit of the other attackers, who fled following the shoot-out," Kenya Defence Forces spokesman Willy Wesonga told AFP.
The attack took place near Ras Kamboni on the Kenya-Somalia border, he added.
Since then, the east African nation has suffered a string of attacks, including one on the Westgate mall in September 2013 in which 67 people were killed.