According to Citizen TV, she disappeared from campus in February 2016 to stay with a Somali family in South B, where she was arrested last week.
She was suspected to have undergone radicalisation after an unidentified agency promised to finance her studies at the International University of Africa in Sudan.
The court ruled on Monday that she remain in custody until a bond of KES 500 000 was paid.
Kavaya was arrested just a few days after police bust a ring of medical interns who were planning a biological attack on Kenya using anthrax.
A man, said to be the leader of the interns, Mohammed Abdi Ali, was said to have been engaging in the active radicalization and recruitment of university students and other Kenyan youths into terrorism networks. He also helped them secretly leave for Libya and Syria to join ISIS fighters.
In February, another Kenyan university student was arrested while on his way to Libya to join the group.
The biochemistry student at the University of Nairobi had used part of his fees to buy his ticket to Sudan, where he would board a connecting flight.