"I heard a loud explosion and then there was black smoke. People started shouting but no one stopped the concert," one witness said.
"They just isolated the place around the explosion and emergency vehicles began coming."
Viktor Sirenko, chief doctor of the city's emergency hospital, said that three people were in a serious condition.
"We are struggling to save their lives," he said.
Tens of thousands of people were atttending the concert at the Hero City memorial, which commemorates Minsk's suffering during the second world war.
Vladimir Naumov, the Belarussian interior ministry, said that police later found an another unexploded homemade bomb in the same area.
The cardboard juice carton contained explosives along with nuts and bolts, similar to the which exploded.
"It had many fingerprints and other traces that could allow us to solve the crime," Naumov said.
A criminal inquiry has been opened, with Anatoly Kuleshov, the Minsk police chief, telling ITAR-TASS he suspected "hooliganism." Bomb experts were sifting through debris at the scene, Russian news agencies reported.
"I think that the explosion was organised by a hooligan who didn't like our beautiful and well-organised party," Kuleshov said.
The opposition Belarussian People's Front urged Alexander Lukashenko, Belarus's president, against using the incident to crack down on the opposition and further limit freedoms.
"It would be a major mistake if the authorities use this reprehensible event to further limit freedom and democracy and for a crackdown against political mistake," Vintsuk Vecherko, the deputy head of the party, told the AFP news agency.