"As you know, an act of terror took place in Saint Petersburg yesterday," he said at a meeting of military officers in the Kremlin.
The homemade bomb went off in a locker at the supermarket yesterday, officials said.
Anna Mityanina, vice governor of Saint Petersburg, which is Russia's second city, said on Twitter that of the 13 wounded eight remained in hospital care.
Five people declined to be hospitalised, she added.
The explosion occurred at around 1845 local time as Russians geared up to celebrate the New Year -- the country's biggest holiday -- followed by Russian Orthodox Christmas, which falls on January 7.
Officials earlier said 10 people had been injured, saying the bomb had the power equivalent to 200 grammes of TNT.
In a sign of the severity of the situation, the case was overseen by Russia's National Anti-Terror Committee even though authorities initially opened a probe into the attempted murder.
The committee said the explosion went off after "a criminal placed an unidentified explosive device in a storage locker."
The blast comes after a suicide bombing killed 15 people and wounded dozens on the Saint Petersburg metro in April.
That bombing was claimed by a group linked to Al-Qaeda which said it was a message to countries engaged in war with Muslims, a veiled reference to Russia's military campaign in Syria.
Earlier this month Russia's FSB security service said it had arrested members of the Islamic State group who had planned to blow up the Kazan Cathedral, one of Saint Petersburg's most famous landmarks, among other crowded places.
The Kremlin has said that those attacks were prevented thanks to intelligence provided by America's Central Intelligence Agency.
Saint Petersburg, Russia's former Imperial capital, will host World Cup matches next year.