The site was hacked on Thursday and Friday by a group calling itself the Sri Lanka Youth.
It demanded that A-level exams due to be held in April be rescheduled because they clashed with Sinhala and Tamil New Year celebrations.
The student, 17, is being questioned to determine any other motives.
A message posted by the group in Sinhala protested about new exam times and called on the president "to take care of the security of Sri Lankan websites or... face a cyber war".
"If you cannot control the situation, hold a presidential election," the message said, along with a call for the president to "stop the prime minister's irresponsible work and look more into the problems of the university students".
It was removed soon after it appeared, the Daily News reported, alongside a message notifying users that the site was temporarily out of service so that it could be maintained.
But soon after it was back in action it was hacked once again, this time with no message.
The BBC's Azzam Ameen in Colombo says that several government websites have recently been hacked and the latest example has prompted people to question why the security of the president's website was so inadequate that it could be overwhelmed by a teenager.
President Sirisena came to power last year.
The presidential website was functioning normally on Monday.