The ministry said Monday, "A team of police investigators are working at the scene. The fact of the event has been entered in the single register of pre-trial investigations, efforts are under way to investigate all circumstances of this incident."
No one has yet claimed responsibility for the attack.
Kernes was shot in the back around noon on Monday, reportedly while bathing in the springs in Kharkiv. The gunshot wounds caused significant injuries.
His press secretary, Tetiana Hruzynska, told Interfax-Ukraine that "Doctors are fighting for his life."
According to a doctor at the hospital where Kernes was admitted, "The injury is very serious: it is a thoraco-abdominal injury, a number of organs have been damaged. Bleeding and collapse. The bleeding has been stopped, and intensive care doctors are now fighting the collapse."
Kernes has been the mayor of Kharkiv since 2010.