The military said some of the pupils wounded in the attack were aged 15 and 16.
The three deaths occurred when a second artillery shell fell nearby several hours later.
Mines killed four other civilians and two government soldiers in Jaffna and the northern district of Vavuniya, according to the defence ministry.
|"The ceasefire agreement put this draconian act to sleep for a while. Now the dragon is given life"|
Daya Master, Liberation Tigers of Tamil Eelam media co-ordinator
The Tamil Tigers have not responded to the military's claims that they were responsible for the attacks.
The Liberation Tigers of Tamil Eelam said on Wednesday that ordinary people would suffer and the government would face a backlash for reinstating the prevention of terrorism act.
"The ceasefire agreement put this draconian act to sleep for a while. Now the dragon is given life," Daya Master, Liberation Tigers of Tamil Eelam (LTTE) media co-ordinator, told Reuters before news of the attack.
"It is nothing but natural that Tamil youths, not necessarily the LTTE alone, would resort to armed defence again.
"What the government has actually done is restart a vicious cycle. It is the nation and the people who are going to suffer."
Last week, Velupillai Prabhakaran, the Tamil Tiger leader, declared that the separatists were resuming their independence struggle.
More than 3,400 people have been killed by the conflict in Sri Lanka in the past year, and the Tamil Tigers' struggle for an independent state has claimed more than 60,000 lives since 1972.