"Today in the centre of Vladikavkaz an explosion occurred as a result of which 11 people were killed," the investigative unit of the Prosecutor General's Office said in a statement.
"A criminal case has been opened ... [for] murder and terrorism."
Emergency services said 28 injured people had sought medical help.
In the immediate aftermath, bodies could be seen lying in the road around the badly damaged white public minibus.
"We were standing at the stop waiting for our minibus when an explosion banged nearby," Jerassa Gagloyeva, a 19-year-old student who was slightly injured in the blast, said.
"We were so scared we just ran away. When the initial shock passed we turned for medical assistance."
North Ossetia borders Chechnya as well as Georgia's breakaway South Ossetia region, the focus of a war in August between Russia and Georgia.
It has been the site of several bomb blasts since the start of Russia's conflict with Chechen separatists which began over a decade ago.
The United States called the incident "a heinous act of terrorism" and sent its condolences to the families of the victims and the government of Russia.
"There can be no justification for such terrorism," Robert Wood, US state department spokesman, said in a statement.