The arrest comes just hours after President Uhuru Kenyatta ordered police to pursue the killers of 7 students and a night guard at the school.
The suspect - a suspended student at the school in Lokichogio - was arrested before irate locals forced their way into the police station and dragged him from his cell.
A key suspect was a senior at the school who was suspended last week after he was found fighting and vowed to take revenge, Kibunja said.
The student was only identified as Abraham and, according to Mr Matata, is from the Toposa tribe of South Sudan.
Regional criminal investigations chief Gideon Kibunja said Saturday's dawn attack occurred at Lokichogio Mixed Secondary School near the countries' border.
India failed to cause problems for opponents, says Luis Norton De Matos
As I had said, there is a big gap between us and other teams in our group. "But the third goal is the punishment for us. In the country's maiden appearance in any World Cup, India showed sparks in patches, but lagged way behind in class.
Reports indicate Lojore had been recalled before he hatched the attack against students he claimed were behind his woes.
While condoling with the parents, teachers and students, Turkana Governor Josphat Nanok asked the national government to allocate boarding schools armed security personnel. "The security arms should follow the matter to ascertain the true motive and bring those behind it to book", he said.
"They sustained abdominal penetrative injuries and require quick medical attention", said Turkana County Referral Hospital superintendent, Dr Gilchrist Lokoel, who is coordinating with the team at the school.
The Kenya Red Cross says it has evacuated the injured.
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