Officials at the Skinners' Kent Academy and Skinners' Kent Primary School said they "cannot be sure" exactly what information hackers have access to.
But they urged parents at the Tunbridge Wells schools to contact their banks to let them know that personal details could have been taken.
The police and the trust's own data protection company are also carrying out inquires after the attack, which began last Wednesday.
It said they did not "appear" to have access to the School Information Management System, which is where personal records for pupils, students and staff are held.
As staff no longer hold vital information on the pupils - including emergency contact details - the decision was taken to close the schools on Monday.
The schools must also have their computers reconfigured so staff can access the resources required to teach. The schools set up remote learning on Tuesday.