The explosion, which police have attributed to 'hooliganism', went off in the middle of a crowd at an open-air concert in central Minsk attended by President Lukashenko.
"An investigation has established that three people injured in the July 3-4 blast in Minsk were in the same area as the president of Belarus," Belta said, citing a source in the Interior Ministry.
"The casualties were not far from the head of state, and they were within the effective range of the explosive device," the source said.
However, the source added that law enforcement bodies did not consider the blast to be an assassination attempt on Lukashenko.
Doctors have not given details on the amount of injuries, but a police source said no one was seriously hurt. No deaths have been reported.