The Class XI student, who was apprehended late last night, allegedly committed the crime as he wanted to get a scheduled parent-teacher meeting and an examination postponed, a CBI spokesperson said.
Pradyuman, a class II student of the school, was found dead with his throat slit by a sharp-edged weapon on the morning of September 8.
The weapon used in the crime has been seized.
"We have come to the conclusion on the basis of CCTV, forensic evidence and scientific evidence. The student has been apprehended. He remains our prime suspect," the spokesperson said.
The juvenile student, who is about 16 years old, was apprehended late last night and his parents were kept in the loop all through, the agency said.
Police in Gurgaon had arrested school bus conductor, Ashok Kumar, for the crime the same day.