Officials imposed the curfew an hour-and-a-half before the end of polling on Monday, after Kirkuk's Kurds flocked to polling stations in a celebratory mood.
The vote is expected to deliver a resounding result in favor of independence.
The independence referendum in Iraq's autonomous Kurdish region proceeded despite warnings by Prime Minister Haider al-Abadi, Turkey, Syria, Iran and the US that the ballot could result in cross-border destabilization.
With opposition to the vote simmering among Arabs and Turkmen who live in the mixed city, there had been rumors that the vote might not go ahead in some parts of town.
Voting was open to up to 5.2 million registered Kurds, including those living abroad, as well as resident non-Kurds, according to the referendum commission. Results are due within 72 hours.
Read more: What is the Iraqi Kurdish referendum?
The majority Kurdish region's president, Masoud Barzani, on Sunday asserted that voting would be peaceful, but acknowledged that the path to independence would be "risky."
'Waiting 100 years'
Queuing in Irbil, the region's capital, one voter who gave his name as Rizgar said: "We have been waiting 100 years for this day."
"God willing, we will say yes, yes to dear Kurdistan," he said.
"I feel so great and happy; I feel we'll be free," said Suad Pirot, a Kirkuk Kurdish resident. "Nobody will rule us. We will be independent."
But in Sulaimaniya, a bastion for political groups opposed to Barzani, queues were shorter.
"I will not vote, the referendum is not good, it could be dangerous because of the threat from Turkey and Iran," said shop owner Ali Ahmed.
Iraqi premier al-Abadi in a televised address Sunday night described the non-binding referendum as "unconstitutional."
"It threatens Iraq, peaceful coexistence among Iraqis and is a danger to the region," al-Abadi said.
A decision by the Kurdistan Regional Government (KRG) to include oil-rich Kirkuk - which is claimed by both the KRG and the Iraqi government - in the vote has prompted speculation that Barzani is seeking to incorporate it into a future Kurdish state.
Last week, the US State Department warned Barzani's administration that "holding the referendum in disputed areas is particularly provocative and destabilizing."
Oil exports threatened
Turkey on Monday swore that it would ignore the referendum, in an indirect reference to aspirations among its own Kurdish minority.
The Turkish foreign minister urged the international community not to recognize the Kurdish ballot and urged Iraqi Kurdish leaders to abandon "utopic goals."
On Monday, Turkey imposed tight controls on its southeastern border gate at Habur to arrivals from northern Iraq.
President Recep Tayyip Erdogan said Turkey at its border controlled the valve for exports of Kurdish oil.
"The valve is with us. It's finished the moment we close it," Erdogan said, adding that "our military is not (there) for nothing."
Last week, Turkish armed forces began a military drill in the region around the border town of Silopi.
Syria's foreign minister, Walid al-Moallem, on Sunday described the referendum as "unacceptable," adding that Damascus only recognized a unified Iraq, according to the Syrian state news agency SANA.
Before its civil war erupted in 2011, Syria's Kurdish population made up around 15 percent of the population. Last week, Kurds held local elections in areas under their control.
Independence has been a long-held dream of Kurds, who also form sizeable minorities in Turkey, Iran and Syria as well as Iraq.
In the wake of World War I, colonial powers, notably France and Britain, redrew the map of the Middle East denying the Kurds statehood.
For decades, the Kurds have been closely allied with the United States, which, however opposes Kurdish moves toward independence.
Kurdish forces played a major role in driving Islamic State (IS) extremists from much of northern Iraq, including Mosul, Iraq's second largest city.
ipj/kms (AP, Reuters, AFP)