Zeid Raad Al Hussein described the incident, in which 10 people were wounded, as "extremely shocking".
Cizre has been the focus of an offensive by Turkey's army against the Kurdish rebel group, the PKK.
Mr Al Hussein also expressed concern over reports that the man who filmed the incident was arrested.
"Filming an atrocity is not a crime but shooting unarmed civilians most certainly is," he said.
"It is essential that there is a thorough, independent, impartial investigation into this and any other events that have led to the wounding or killing of civilians."
The incident in Cizre, a predominantly Kurdish city, occurred on 20 January. Video footage posted online purporting to be of the immediate aftermath of the shooting shows people being loaded into ambulances amid screaming and the sound of explosions.
Reports suggested that the group who came under fire were attempting to rescue people wounded in an earlier clashes.
The video footage also appears to show that some of the group were pushing a cart loaded with bodies across the street, watched by an armoured military vehicle.
Mr Al Hussein, the UN High Commissioner for Human Rights, said the victims had been "apparently cut down in a hail of gunfire".
The unrest came just days after security forces killed 20 Kurdish militants in clashes in nearby Diyarbakir, according to the Turkish military.
Three Turkish soldiers also died in a rebel attack, the military said.
The region has suffered its worst violence in two decades since a ceasefire between the Turkish government and the PKK collapsed in July.
The PKK, which has fought for autonomy for Turkey's Kurdish minority for decades, has been attacking security forces, while the army has been besieging Kurdish-dominated towns.
The Turkish Human Rights Foundation says at least 198 civilians, including 39 children, have died in areas under curfew since August.
Since July, more than 200 Turkish soldiers and policemen have been killed in attacks by the PKK, which is listed as a terrorist organisation by Turkey, the EU and US.
The European Union has called for an immediate ceasefire.
The top UN human rights official has urged Turkey to investigate an apparent shooting by security forces of unarmed civilians in the city of Cizre.