Putin made the comments at an award ceremony in Moscow for Russian military members who fought in Syria.
Svetlana Petrenko, a spokeswoman for the Investigative Committee of Russia, told Interfax that an improvised device containing the equivalent of 200 grams of TNT detonated in one of the port city's supermarkets. The device included "lethal fragments" to increase casualties, the Russian Investigative Committee said.
Russia's National Antiterrorism Committee (NAK) said the explosion occurred at 6:45 p.m. local time in a customer locker area at the city's Perekrestok supermarket.
Authorities said the suspect was caught on surveillance video leaving a backpack at the market's coat check.
State news agency TASS, citing Alexander Klaus, head of the Investigative Committee's St. Petersburg office, initially reported that 10 people had been hospitalized.
"The wounded people’s lives are not in danger," Klaus apparently told reporters at the scene.
In the wake of the explosion, Interfax said the Investigative Committee's St. Petersburg office has opened a criminal investigation into the attempted killing of two or more people.