Cizre was sealed off since last Friday after the Turkish army launched an operation against Kurdish militants there.
Civilian casualties have been reported and there are concerns about food shortages.
The Council of Europe has asked Turkey to allow access to observers.
Amid the operation against the PKK (Kurdistan Workers’ Party), Cizre locals have also complained of shortages of water and electricity. People have also been unable to bury their dead.
A statement from the local authorities thanked Cizre residents for their patience during the “successful operation against the terror organisation”.
Twenty civilians have died since Friday, eyewitnesses said, although the government has said only one civilian died and that the rest were militants.
Turkey has described Cizre as a hotbed of PKK activity, with one official saying they believed 80 professional PKK fighters were operating there and around 200 young people had taken up arms.
But Selahattin Demirtas, the leader of Turkey’s main pro-Kurdish party, has described the curfew as a “death sentence” for Kurds in the Kurdish-majority city of 100,000 people.
One doctor, who is responsible for more than 4,000 patients but cannot leave his home, told the BBC that the emergency department at the state hospital was closed and pharmacies were not opening.
Violence has surged between the Turkish government and the PKK since a ceasefire collapsed in July.
On Friday, an attack on a cafe in the mainly Kurdish city of Diyarbakir left a waiter dead and three policemen injured.
More than 40,000 people have died since the PKK launched an armed campaign in 1984, calling for an independent Kurdish state within Turkey.