Local media initially had reported that a total of 12 people, including a shooter, had been killed.
"When we arrived at the scene we saw nine dead bodies, including two children, and another two passed away on their way to the hospital," Andrijana Nastic, a state prosecutor, told Vijesti TV.
Nastic did not say how old the children killed were and could not reveal details regarding the identities of the victims. Media reported earlier that a policeman had been among the injured.
"I can only say that the shooter was killed by a citizen (civilian)," Nastic said. Media earlier had reported that police had killed the shooter.
Media reported a man from Cetinje had opened fire at random in his neighbourhood after a family dispute.
Montenegro's Prime Minister Dritan Abazovic said a three-day mourning period would be declared in the country starting Friday evening.
"I was deeply disturbed with reports about terrible tragedy in Cetinje. I express my deepest condolences to those families affected and all those who lost their loved ones," President Milo Djukanovic tweeted.
(Reporting by Ivana Sekularac;Editing by Alexander Smith and Paul Simao)
